<PAGE>
 
                                                                    EXHIBIT 10.4

                              SECOND AMENDMENT TO
                             AMENDED AND RESTATED
                         ACCOUNTING AND ADMINISTRATIVE
                              SERVICES AGREEMENT


          This Second Amendment to Accounting and Administrative Services
Agreement ("Second Amendment") is made and entered into this 25/th/ day of June,
1998 by and between Einstein/Noah Bagel Corp., a Delaware corporation (the
"Company"), and Boston Chicken, Inc., a Delaware corporation ("BCI").


                                   RECITALS
                                   --------

          The Company and BCI are parties to an amended and restated accounting
and administrative services agreement dated May 28, 1996, as amended (the
"Services Agreement").  The parties have previously agreed to extend the term of
the Services Agreement past March 26, 1998, on a month-to-month basis, and the
parties now desire to extend the term of the Services Agreement to May 31, 1999
and to amend the Services Agreement as hereafter set forth.


                                   COVENANTS
                                   ---------

          In consideration of the matters recited above and the mutual covenants
of the parties, the parties hereto agree as follows:

          1.1  Amendment. The Services Agreement shall be amended as of the date
               ---------                                  
hereof as follows:

               (a) The Services Agreement is amended by changing "Einstein Bros.
     Bagels, Inc." to "Einstein/Noah Bagel Corp." and "EBBI" to "ENBC" each
     place where such terms appear.

               (b) Section 1.1 of the Services Agreement is hereby amended by
     deleting clause (b).
 
               (c) Section 2.1 of the Services Agreement is hereby amended by:

                   (i)    deleting clauses (h), (i), (j) and (l) therefrom;
                   (ii)   relettering clause (k) as clause (h); and
                   (iii)  adding the following clause (i):
 
                          "(i) administration and maintenance of corporate
               payroll, and administration of the processing of payroll and
               calculation of applicable tax and other withholdings relating to
               the Units or Entities."
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          (d) Section 3.1 of the Services Agreement is hereby amended by
     deleting such section in its entirety and substituting therefor the
     following:

          "3.1(a) In consideration of the Services and Admin. Items, ENBC agrees
          to pay to BCI an accounting and administrative fee per four- or five-
          week accounting period of BCI ("Accounting Period"), which shall be
          determined for fiscal 1998 by taking the "ENBC Portion" of fees for
          Accounting, Payroll & Admin. and Peoplesoft for 1998, as shown on
          Exhibit B hereof, deducting therefrom fees previously paid by ENBC
          hereunder for fiscal 1998 and dividing the balance by the number of
          Accounting Periods remaining in fiscal 1998 for which ENBC has not yet
          made payment. Such fee shall be determined for Accounting Periods
          after fiscal 1998 by taking the "ENBC Portion" of fees for Accounting,
          Payroll and Admin. and Peoplesoft for the applicable fiscal year (as
          set forth on a revised Exhibit B prepared by BCI, based on its budget
          for such fiscal year, in the same manner as Exhibit B hereof) and
          dividing such amount by 13. All such fees shall be subject to
          adjustment as provided in Section 3.1(b) hereof.

          3.1(b)  To the extent BCI's actual overhead for its accounting
          department, payroll and administration departments and its
          "Peoplesoft" project (including, without limitation, any salary bonus,
          severance or other compensation paid to employees assigned to such
          departments or projects but excluding severance paid to employees
          terminated prior to fiscal 1998) for any fiscal quarter is greater or
          less than the applicable proportion of the amount shown on Exhibit B
          for such category of overhead, then the fees payable pursuant to
          Section 3.1(a) hereof for such fiscal quarter shall be recomputed, in
          the manner provided in Section 3.1(a), and any difference shall be
          paid to the party entitled thereto in three equal increments over the
          three Accounting Periods following the fiscal quarter for which such
          adjustment is made. BCI agrees to give ENBC upon ENBC's request all
          information reasonably requested by ENBC regarding the amounts BCI has
          budgeted or incurred for the foregoing overhead categories.

          (e)     Section 4.1 of the Services Agreement is hereby amended by
     deleting such section in its entirety and substituting therefor the
     following:

          "4.1(a) The term of this Agreement shall expire on May 31, 1999,
          unless the parties mutually agree to extend such term; provided that
          either party may terminate this Agreement during the term upon 180
          days' prior written notice to the other party; provided, further, that
          BCI may terminate this Agreement without notice and cease rendering
          the Services and Admin. Items hereunder 15 days after notice of any
          non-payment of the fees and expenses provided for herein when such
          fees and expenses are          

                                       2
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          due and payable, unless such non-payment is cured within such 15 day
          period. In connection with any termination of this Agreement (except
          where termination is based on ENBC's non-payment of fees and
          expenses), BCI agrees to provide to ENBC, at ENBC's expense, all
          assistance that may be reasonably requested by ENBC to assist ENBC in
          effecting a smooth and orderly transition from the provision of
          services hereunder by BCI to the provision of such services by ENBC
          employees or other service providers. In addition to the foregoing,
          and notwithstanding anything to the contrary, in the event that BCI
          sells to a third party that is not an affiliate of BCI all or the
          majority of its shares in ENBC and such third party purchaser desires
          to transition all of the services described in this Agreement away
          from BCI or desires to relocate ENBC's support center, this Agreement
          may be terminated on 90 days' notice (a) in either event by ENBC, at
          the direction of such purchaser or (b) by BCI in the event of a
          relocation of ENBC's support center.

          4.1(b) BCI and ENBC further agree that in the event ENBC gives notice
          to BCI that ENBC desires to cease the purchase of such services as it
          may specify in such notice (but less than all of the services being
          provided by BCI hereunder), then BCI and ENBC agree that (i) ENBC
          shall be permitted to cease purchasing such services within a
          reasonable period of time (but in any event not more than 90 days),
          provided that BCI has not reasonably concluded that the discontinuance
          of such services would materially interfere with its ability to
          continue to provide other services that it is obligated to provide
          hereunder, and (ii) they shall negotiate in good faith to determine
          the amount by which ENBC's fees hereunder should be reduced, it being
          agreed that ENBC shall be entitled to a reduction in such fees to
          reflect the marginal reduction to BCI in the overhead necessary to
          provide services hereunder resulting from the discontinuance of such
          services."

     2.1  Continuing Effect of Services Agreement.  The Services Agreement, as
          ---------------------------------------                             
amended hereby, is ratified and confirmed and remains in full force and effect.

     3.1  GOVERNING LAW.  THIS SECOND AMENDMENT SHALL BE CONSTRUED IN ACCORDANCE
          -------------                                                         
WITH AND GOVERNED BY THE LAWS OF THE STATE OF COLORADO APPLICABLE TO CONTRACTS
MADE AND TO BE PERFORMED THEREIN WITHOUT REGARD TO THE CONFLICTS OF LAW
PROVISIONS THEREOF.

     4.1  Counterparts.  This Second Amendment may be executed in counterparts,
          ------------                                                         
each of which shall be deemed an original, but each of which together shall
constitute but one and the same instrument.

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     5.1  Headings.  The headings of the sections of the Second Amendment are
          --------                                                           
inserted for convenience only and shall not be deemed to constitute a part of
this Second Amendment.


     IN WITNESS WHEREOF, the parties have executed this Second Amendment to be
effective on the date provided herein.


BOSTON CHICKEN, INC.                     EINSTEIN/NOAH BAGEL CORP.


By: /s/ Michael R. Daigle                By: /s/ Paul A. Strasen
    -------------------------                -----------------------
Its:Senior Vice President and            Its:Senior Vice President
    -------------------------                -----------------------  
    General Counsel
    ---------------

                                       4
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<TABLE> 
<CAPTION> 
1998 ENBC/BCI
Fees Enbc Fee
 Calculation
Exhibit B

            Allocation Factors                           ENBC Fee Calculation
  -----------------------------------         --------------------------------------------------------------------------------------
                                                                                             Basis for                     ENBC    
  Number of Stores                                                          1998 Budget      Allocation      Factor       Portion 
  ----------------                                                         -------------    ------------    --------    ------------
  <S>                                                                      <C>              <C>             <C>         <C> 
  -   Number of BM Stores       1,150  68% ^                                                              
      Number of EMBC Stores       250  32% ^  Systems                       $12,080,000       #  Stores         32%      $3,908,235 
                               -------                                                                   
                                1,700                                                                    
                                              Accounting                     $2,658,252       #  Stores         32%        $860,023
  Number of People (12/31/97)                                                                            
      Number of BM People       69% ^         Payroll & Admin.              
      Number of ENBC People     31% ^         (Including Teleservices)       $2,594,395       #  People         31%        $804,262
                               -------                                                                   
                                100%          PeopleSoft Project Set-up                                  
                                              (less Hardware)*               $2,016,718            Half         50%      $1,008,359
                                                                                                         
                                              PeopleSoft Project                                         
                                              Hardware                         $470,000       #  People         31%        $146,700
                                                                           -------------                                ------------
                                              Total BCI Budget              $19,819,365                                  $6,726,679




                                              * BCI shall include $939,236 of its PeopleSoft Development Cost in its 1999 budget and
                                              $704,427 of its PeopleSoft Development Cost in its 2000 budget. Such amounts
                                              represent financed project costs payable by BCI after 1998, and shall be allocated 50%
                                              to ENBC. In the event the agreement is terminated prior to the time ENBC's share of
                                              such amounts has been recovered by BCI, then ENBC shall pay the remaining amounts to
                                              BCI at a rate of $117,405 per fiscal quarter. BCI agrees to take all actions required
                                              under its agreement with PeopleSoft, Inc. to assure that ENBC shall not have any
                                              obligation to PeopleSoft to pay license fees for Peoplesoft software provided to ENBC
                                              hereunder, including without limitation executing and delivering appropriate
                                              assignment documents under Section 13 of such agreement.
</TABLE>