Skyrim:Destroy the Dark Brotherhood!

Quick Walkthrough
#While in the Abandoned Shack during the quest With Friends Like These..., kill Astrid instead of a hostage.
#Travel to any city and talk to a guard.
#Speak to Commander Maro in Dragon Bridge southwest of Solitude.
#Travel to the Dark Brotherhood Sanctuary and kill all Dark Brotherhood members inside.
#Return to Commander Maro and collect your reward.

Detailed Walkthrough
Complete Innocence Lost by killing Grelod the Kind. When you are kidnapped by the Brotherhood and brought to the Abandoned Shack, kill Astrid instead of a hostage and this quest will begin.

After Astrid's death, travel to any city and speak to a guard. Inform them that you killed the Dark Brotherhood's leader, and you will be directed to speak to Commander Maro in Dragon Bridge southwest of Solitude. He can be found in the Penitus Oculatus Outpost.

After speaking to Commander Maro, you will be given the passphrase ("Silence, my brother") to their hideout and directed to kill everyone inside. He says that you should "have the honor" of clearing out the place, meaning you'll be going in alone.

Travel to the Brotherhood Sanctuary and kill everyone inside. It should be relatively simple, as this quest will have them spread out between each room (as opposed to them being gathered and chatting when you first enter as an actual member). Loot what you please: you have access to an Iron Battleaxe of Chills on Arnbjorn, one of the twenty-four "unusual gems" or Stones of Barenziah needed for the quest No Stone Unturned, the Alteration skill book Sithis, many poisons lying around, four different soul gems, part of the Marked for Death shout, and the Dark Brotherhood armor.

Reward
Return to Commander Maro in Dragon Bridge, and he will be overjoyed and reward you with 3,000 gold, regardless of your level. He will also make sure that the Emperor himself hears of your accomplishments.

Notes
Astrid has a rather lengthy animation when she jumps off the bookshelf. She is able to be attacked, but will not attack during it, making her quite an easy kill.
If you have the Misdirection perk, you can rob Astrid of her gear before you attack her, making her extremely easy to kill. 
Naturally, beginning this quest forever bars you from joining the Dark Brotherhood. Destroying the Dark Brotherhood prevents access to a number of lucrative quests.  It does yield a good amount of valuable loot, though most of it is also available if you join them.
In particular, destroying the Brotherhood means you can never gain access to Shadowmere, the Summon Spectral Assassin power, the essential Dark Brotherhood Initiate followers, or the Master trainers for Alchemy and Light Armor, in addition to Cicero's offer of being a follower.
Babette, Cicero, and the Night Mother won't be in the sanctuary during the attack.
If the player successfully casts Calm on a member of the brotherhood, they will offer the same dialogue as if the player had joined the brotherhood, with the exception of Nazir, who will not offer contracts.
Either joining the Dark Brotherhood or destroying it will prevent further assassination attempts against you.
If they are all together, the members of the Dark Brotherhood are a challenge to fight, so attacking one or two at a time is advised.
It is not possible for followers to pass through the black door, meaning they cannot enter the sanctuary with you. However, spectral entities such as Arniel's spirit and the ghostly Dragon Priest (summoned by the Konahrik mask) will enter with you.
After completing this quest, guards will occasionally comment on your accomplishment. See the Guard Dialogue page for specifics.

Bugs
 
 Typing   in the console resolves this problem, and starts this quest.
 
 

Quest Stages