Place the butter and chocolate in a microwave-safe bowl. Heat in the microwave at half-power in 30-second increments until the butter has melted and the chocolate melts when stirred. Stir until smooth, and set aside to cool slightly. 

Whisk in the cocoa powder, followed by the sugar, and then the eggs and vanilla. Then, mix in the flour and salt.

Stir in the cookie pieces.

Transfer the batter to the prepared pan, and spread it evenly. Bake 30 to 35 minutes, or until a pick inserted into the center comes out with a few moist crumbs. 

Set the pan on a wire rack, and allow the brownies to cool completely.

Using an electric mixer on medium speed, beat the butter until creamy. Slowly add the confectioners’ sugar, and mix until smooth.

With the mixer on low speed, add the milk, vanilla, and salt, and mix until combined. If your frosting is too thick to spread, you can add small amounts of milk until it's the desired consistency. 

Increase the mixer speed to high and beat the frosting until fluffy and smooth.

Fold in the cookie crumbs.

Spread the frosting over the cooled brownies, and top with more cookie pieces.