<PAGE>   1
                                                                   EXHIBIT 10.20

                         DREYER'S GRAND ICE CREAM, INC.

                            STOCK OPTION PLAN (1993)
                            as amended May 12, 1999*

1.       Purpose

         The purpose of the Plan is to provide a vehicle under which a variety
of stock option awards may be granted to employees and directors of the Company
and its Subsidiaries to further the profits and prosperity of the Company and
its Subsidiaries.

2.       Definitions

         A. "Award" means any form of stock option granted under the
         Plan.

         B. "Award Notice" means any written notice from the Company
         to a Participant or agreement between the Company and a
         Participant that establishes the terms applicable to an Award.

         C. "Board of Directors" means the Board of Directors of the
         Company.

         D. "Code" means the Internal Revenue Code of 1986, as
         amended.

         E. "Committee" means the Compensation Committee of the Board of
         Directors, or such other committee designated by the Board of
         Directors, which is authorized to administer the Plan under Section 3
         hereof. The Committee, and any separate committee to which it delegates
         any of its authority and duties under the Plan, shall each have
         membership composition which enable the Plan to qualify under Rule
         16b-3 with regard to Awards to persons who are subject to Section 16 of
         the Exchange Act.

         F. "Common Stock" means common stock of the Company.

         G. "Company" means Dreyer's Grand Ice Cream, Inc., a
         Delaware corporation.

         H. "Director" means a member of the Board of Directors.

--------
         *Also reflects adjustments for October 30, 1997 two-for-one stock
split.

                                        1
<PAGE>   2

         I. "Exchange Act" means the Securities Exchange Act of 1934, as
         amended.

         J. "Fair Market Value" means, as of a specified date, the mean of the
         high and the low sales price of one share of Common Stock on the
         over-the-counter market or the closing price on the principal stock
         exchange where the Company's stock prices are officially quoted, or if
         not traded on that date, then on the date last traded. If for any
         reason the Company's stock ceases to be traded on the over-the-counter
         market or listed on a stock exchange, the Committee shall establish the
         method for determining the Fair Market Value of the Common Stock.

         K. "Key Employee" means any employee of the Company or a Subsidiary
         responsible for the management of the business of the Company (or a
         Subsidiary) who is in a position to make substantial contributions to
         the sound performance of the Company (or a Subsidiary). The term "Key
         Employee" shall include officers as well as other employees devoting
         full time to the Company (or a Subsidiary) and shall include Directors
         who are also active officers or employees of the Company (or a
         Subsidiary).

         L. "Non-Employee Director" means a Director who is not an employee of
         the Company or a Subsidiary.

         M. "Participant" means any individual to whom an Award is granted
         under the Plan.

         N. "Plan" means this Plan, which shall be known as the Dreyer's Grand
         Ice Cream, Inc. Stock Option Plan (1993).

         O. "Rule 16b-3" means Rule 16b-3 issued under the Exchange Act or any
         successor rule.

         P. "Subsidiary" means a corporation or other business entity (i) of
         which the Company directly or indirectly has an ownership interest of
         50% or more, or (ii) of which it has a right to elect or appoint 50% or
         more of the board of directors or other governing body.

3.       Administration.

         A. The Plan shall be administered by the Committee.  Subject
         to the terms and conditions of this Plan, the Committee shall
         have the authority to:

            (i) interpret and determine all questions of policy and expediency
            pertaining to the Plan;

                                        2
<PAGE>   3

                  (ii)   adopt such rules, regulations, agreements and
                  instruments as it deems necessary for the Plan's proper
                  administration;

                  (iii)  select Key Employees to receive Awards;

                  (iv)   determine the form and terms of Awards;

                  (v)    determine the number of shares subject to Awards;

                  (vi)   determine whether Awards will be granted singly, in
                  combination, in tandem, in replacement of, or as alternatives
                  to other grants under the Plan or any other incentive or
                  compensation plan of the Company, a Subsidiary or an acquired
                  business unit;

                  (vii)  grant waivers of Plan or Award conditions;

                  (viii) accelerate the vesting of Awards;

                  (ix)   correct any defect, supply any omission, or reconcile
                  any inconsistency in the Plan, any Award or any Award Notice;
                  and

                  (x)    take any and all other actions it deems necessary or
                  advisable for the proper administration of the Plan.

         B. The interpretation and construction of any provision of the Plan by
         the Committee shall be final, conclusive and binding on all parties,
         including the Company, its Subsidiaries and stockholders, and the
         Participants, their estates, executors, administrators, heirs and
         assigns. No member of the Committee shall be liable for any action or
         determination made by him in good faith.

         C. The Committee may adopt such Plan amendments, procedures,
         regulations, subplans and the like as it deems are necessary to enable
         Key Employees and Directors who are foreign nationals or employed
         outside the United States to receive Awards.

         D. The Committee may delegate its authority to grant and administer
         Awards to a separate committee; however, only the Committee may grant
         and administer Awards with respect to persons who are subject to
         Section 16 of the Exchange Act.

                                       3
<PAGE>   4

4.       Eligibility

         A. Any Key Employee is eligible to become a Participant in the Plan.

         B. Non-Employee Directors shall receive Awards in accordance with
         Section 7.

5.       Stock Subject to the Plan.

         A. The aggregate number of shares of Common Stock which may be
         delivered on exercise of options under this Plan shall not exceed six
         million four hundred thousand (6,400,000) shares, subject to
         adjustment as provided hereinafter. If, at any time during the term of
         this Plan, an option granted under this Plan shall have expired or
         terminated for any reason without having been exercised in full, the
         unpurchased shares shall become available for option to other
         employees.

         B. In the event that (i) the number of outstanding shares of Common
         Stock shall be changed by reason of split-ups, combinations or
         reclassifications of shares or otherwise, (ii) any share dividends are
         distributed to the holders of Common Stock or (iii) the Common Stock is
         converted into or exchanged for other shares as a result of any merger,
         consolidation or recapitalization then, in any such case, the number of
         shares for which options may thereafter be granted under this Plan,
         both in the aggregate and as to any individual, and the number of
         shares then subject to options theretofore granted under this Plan and
         the price per share payable upon exercise of such options shall be
         appropriately adjusted by the Committee so as to reflect such change.

         C. The shares of Common Stock available under the Plan may be
         authorized and unissued shares or treasury shares.

6.       Term

         This Plan shall be effective and operative, subject to approval of the
stockholders of the Company within twelve months after its adoption by the Board
of Directors, from the date that the Plan is approved by the Board of Directors
and shall remain in effect until terminated by the Board of Directors.

7.       Awards to Non-Employee Directors

         Non-Employee Directors shall receive awards in accordance with the
following terms:

         A. On the day of adoption of this Plan by the Company's stockholders
         (the "Approval Date"), each Non-Employee Director



                                        4
<PAGE>   5

         shall receive a non-qualified option for 10,000 shares of Common
         Stock.

         B. After the Approval Date, any person who is appointed or elected a
         Non-Employee Director shall receive a non-qualified stock option for
         10,000 shares of Common Stock on the date such person is so appointed
         or elected.

         C. On each anniversary of the Approval Date each Non-Employee Director
         shall receive a non-qualified stock option for 3,000 shares of Common
         Stock.

         D. Options to Non-Employee Directors shall be subject to the following
         terms: (i) the exercise price shall be equal to 100% of the Fair Market
         Value of the Common Stock on the date of the grant, payable in
         accordance with all the alternatives stated in Section 8.B(ii); (ii)
         the term of the options shall be 10 years; (iii) the options shall be
         exercisable beginning 6 months after the date of the grant; and (iv)
         the options shall be subject to Section 10.

8.       Stock Options

         A. Awards shall be granted in the form of stock options. Stock options
         may be incentive stock options within the meaning of Section 422 of the
         Code or non-qualified stock options (i.e., stock options which are not
         incentive stock options).

         B. Subject to Section 8.C relating to incentive stock options, options
         shall be in such form and contain such terms as the Committee deems
         appropriate. While the terms of options need not be identical, each
         option shall be subject to the following terms:

                  (i)   The exercise price shall be the price set by the
                  Committee but may not be less than 100% of the Fair Market
                  Value of the Common Stock on the date of the grant.

                  (ii)  The exercise price shall be paid in cash (including
                  check, bank draft, or money order), or all or part of the
                  purchase price may be paid by delivery of the optionee's
                  delivery of Common Stock, already owned by the Participant for
                  at least six (6) months and valued at its Fair Market Value,
                  or any combination of the foregoing methods of payment.

                  (iii) An option shall be treated as exercised on the later of
                  (i) the date that proper notice of exercise accompanied by the
                  aggregate exercise price is received




                                       5
<PAGE>   6

                  by the Company, or (ii) such exercise date as may be specified
                  in such proper notice when accompanied by such aggregate
                  exercise price.

                  (iv)  The term of an option may not be greater than 10 years
                  from the date of the grant.

                  (v)   Neither a person to whom an option is granted nor his
                  legal representative, heir, legatee or distributee shall be
                  deemed to be the holder of, or to have any of the rights of a
                  holder with respect to, any shares subject to such option
                  unless and until he has exercised his option.

         C.       The following special terms shall apply to grants of
         incentive stock options:

                  (i)   No incentive stock option shall be granted after the
                  tenth (10th) anniversary of the date the Plan is adopted by
                  the Board of Directors.

                  (ii)  Subject to Section 8.C.(iii), the exercise price under
                  each incentive stock option shall not be less than 100% of the
                  Fair Market Value of the Common Stock on the date of the
                  grant.

                  (iii) No incentive stock option shall be granted to any
                  employee who directly or indirectly owns stock possessing more
                  than 10% of the total combined voting power of all classes of
                  stock of the Company, unless the exercise price is at least
                  110% of the Fair Market Value of the Common Stock on the date
                  of the grant and such option is not exercisable after the
                  expiration of 5 years from the date of the grant.

                  (iv)  No incentive stock option shall be granted to a person
                  in his capacity as a Key Employee of a Subsidiary if the
                  Company has less than a 50% ownership interest in such
                  Subsidiary.

                  (v)   Incentive stock options shall contain such other terms
                  as may be necessary to qualify the options granted therein as
                  incentive stock options pursuant to Section 422 of the Code,
                  or any successor statute.

9.       Reload Options

         A. Concurrently with the award of options to any
         Participant, the Committee may authorize reload options
         ("Reload Options") to purchase for cash or shares a number of

                                        6
<PAGE>   7

         shares of the Common Stock.  The number of Reload Options
         shall equal:

                  (i)  the number of shares of Common Stock used to exercise the
                  underlying options; and

                  (ii) the number of shares of Common Stock used to satisfy any
                  tax withholding requirement incident to the exercise of the
                  underlying option, including shares withheld from those that
                  would otherwise be issuable to the optionee pursuant to
                  exercise of the subject option. The grant of a Reload Option
                  will become effective upon the exercise of the underlying
                  options or Reload Options through the use of shares of Common
                  Stock held by the optionee for at least six (6) months.

         B. Notwithstanding the fact that the underlying option may be an
         Incentive Stock Option, a Reload Option is not intended to qualify as
         an "incentive stock option" within the meaning of Section 422 of the
         Code.

         C. Each Award Notice shall state whether the Committee has authorized
         Reload Options with respect to the underlying options. Upon the
         exercise of an underlying option or other Reload Option, the Reload
         Option will be evidenced by an amendment to the underlying Award
         Notice.

         D. The option price per share of Common Stock deliverable upon the
         exercise of a Reload Option shall be the Fair Market Value of a share
         of Common Stock on the date the grant of the Reload Option becomes
         effective.

         E. Each Reload Option is fully exercisable six (6) months from the
         effective date of grant. The term of each Reload Option shall be equal
         to the remaining option term of the underlying option.

         F. No additional Reload Options shall be granted when options or Reload
         Options are exercised pursuant to the terms of this Plan following
         cessation of the optionee's employment with the Company for any reason.

10. Exercise of Stock Option Upon Termination of Employment or Services

         A. Options granted under Section 7 shall be exercisable upon the
         Participant's termination of service within the following periods only.
         Subject to Section 17, stock options to other Participants may permit
         the exercise of options upon the Participant's termination of
         employment within the following

                                        7
<PAGE>   8

         periods, or such shorter periods as determined by the
         Committee at the time of grant:

                  (i)   if on account of death, within 24 months of such event
                  by the person or persons to whom the Participant's rights
                  pass by will or the laws of descent or distribution.

                  (ii)  if on account of disability (as defined in Section
                  22(e)(3) of the Code or any successor statute), non-qualified
                  stock options may be exercised within 24 months of such
                  termination and incentive stock options within 12 months.

                  (iii) if on account of retirement (as defined from time to
                  time by Company policy), non-qualified stock options may be
                  exercised within 24 months of such termination and incentive
                  stock options with 3 months.

                  (iv)  if for any reason other than death, disability or
                  retirement (as defined from time to time by Company policy),
                  options may be exercised within 3 months of such termination.

         B. An unexercised option shall be exercisable only to the extent that
         such option was exercisable on the date the Participant's employment or
         service terminated. However, terms relating to the exercisability of
         options may be amended by the Committee before or after such
         termination, except in respect to options granted under Section 7.

         C. In no case may an unexercised option be exercised to any extent by
         anyone after expiration of its term.

11.      Acceleration of Vesting of Options.

         A. In the event of a Change in Control (as defined below), death of an
         optionee or retirement of an optionee (as defined from time to time by
         Company policy), all options which have not yet vested shall vest,
         mature and become exercisable in whole or in part immediately prior to
         the event constituting the Change of Control, or immediately upon the
         death or retirement of such optionee.

         B. A Change of Control for these purposes shall be defined as, (i) the
         acquisition by any person of beneficial ownership of forty percent
         (40%) or more of the combined voting power of the Company's outstanding
         securities immediately after such acquisition (which forty percent
         (40%) shall be calculated after including the dilutive effect of the
         conversion or exchange of any outstanding securities of the Company

                                        8
<PAGE>   9

         convertible into or exchangeable for voting securities), or (ii) a
         change in the composition of majority membership of the Board of
         Directors over any two-year period beginning with the date of adoption
         of this Plan by the Board of Directors, or (iii) a change in ownership
         of the Company such that the Company becomes subject to the delisting
         of its Common Stock from the NASDAQ National Market System, or (iv) the
         approval by the Board of Directors of the sale of all or substantially
         all of the assets of the Company, or (v) the approval by the Board of
         Directors of any merger, consolidation, issuance of securities or
         purchase of assets, the result of which would be the occurrence of any
         event described in clause (i), (ii) or (iii) above. Notwithstanding
         anything to the contrary in this Section 11.B, acquisitions by any
         person (or any group of which such a person is a member) who is as of
         the date of adoption of this Plan by the Board of Directors, a member
         of the Board of Directors, of beneficial ownership of forty percent
         (40%) or more of the combined voting power of the Company's outstanding
         securities immediately after such acquisition (calculation of such
         forty percent (40%) being made as described above), shall not be deemed
         a Change of Control for purposes of this Plan.

12.      Nonassignability

         The rights of a Participant under the Plan shall not be assignable by
         such Participant, by operation of law or otherwise, except by will or
         the laws of descent and distribution. During the lifetime of the person
         to whom a stock option is granted, he or she alone may exercise it.

13.      Payment of Withholding Taxes

         A. As a condition to receiving or exercising an Award, as the case may
         be, the Participant shall pay to the Company the amount of all
         applicable federal, state, local and foreign taxes required by law to
         be paid or withheld relating to receipt or exercise of the Award.

         B. An optionee may satisfy such withholding requirements in whole or in
         part by directing the Company to withhold shares from those that would
         otherwise be issuable to the Participant or by otherwise tendering
         other shares of Common Stock owned by the Participant. The withheld
         shares and other tendered shares will be valued at the Fair Market
         Value as of the date that the tax withholding obligation arises.

14.      Amendments

         The Board of Directors may amend the Plan at any time and from time to
         time, provided however that the Board shall not amend the

                                        9
<PAGE>   10
         terms of the Plan more frequently than permitted under Rule 16b-3 in
         regard to provisions that affect persons receiving Awards under Section
         7. Rights and obligations under any Award granted before amendment of
         the Plan shall not be materially altered or impaired adversely by such
         amendment, except with consent of the person to whom the Award was
         granted.

15.      Regulatory Approvals and Listings

         Notwithstanding any other provision in the Plan, the Company shall have
         no obligation to issue or deliver certificates of Common Stock under
         the Plan prior to (A) obtaining approval from any governmental agency
         which the Company determines is necessary or advisable, (B) admission
         of such shares to listing on the stock exchange on which the Common
         Stock may be listed and (C) completion of any registration or other
         qualification of such shares under any state or federal law or ruling
         of any governmental body which the Company determines to be necessary
         or advisable.

16.      No Right to Continued Employment or Grants

         Participation in the Plan shall not give any Key Employee any right to
         remain in the employ of the Company or any Subsidiary. Further, the
         adoption of this Plan shall not be deemed to give any Key Employee or
         other individual the right to be selected as a Participant or to be
         granted an Award.

17.      Special Provision Pertaining to Persons Subject to Section 16

         Notwithstanding any other term of this Plan, the following shall apply
         to persons subject to Section 16 of the Exchange Act, except in the
         case of death or disability:

         A. No stock option granted pursuant to the Plan may be exercisable for
         at least 6 months after the date of grant.

18.      Limitations on Awards Under the Plan

         No one Participant shall receive in the aggregate Awards granting him
         more than fifty percent (50%) of the aggregate number of shares
         (6,400,000) which may be delivered on exercise of options under the
         Plan.



                                       10