Preheat oven to 350 degrees F. Line the bottom and sides of an 8-by-8-inch pan with parchment paper, leaving a slight overhang on two sides.
To make the brownies, sift together flour, cocoa powder, and salt in a small bowl and set aside. Melt chocolate and butter in a double boiler or a bowl set over a saucepan of gently simmering water. Stir until smooth, then remove from heat. Add brown sugar and whisk until sugar is dissolved and mixture has cooled slightly. Whisk in eggs and vanilla. Using a large rubber spatula, fold flour mixture into chocolate mixture until just incorporated. Pour into prepared pan. Bake 18 to 20 minutes, or until a toothpick inserted into the middle comes out clean. Transfer pan to a wire rack to cool completely.
For the cookie dough, in a large mixing bowl beat together butter and sugars with an electric mixer on medium speed until light and fluffy, 2 to 3 minutes. Mix in milk and vanilla. Add flour and salt and stir until incorporated. Stir in chocolate chips. Gently spread dough onto cooled brownies, smoothing the top into an even layer. Refrigerate while you prepare the glaze.
For the glaze, gently melt chocolate and butter together in a double boiler or a small saucepan set over low heat. Stir until smooth. Pour over cookie dough, carefully spreading into a thin, even layer. Return pan to refrigerator and chill until set, about 30 minutes.
To remove brownies from pan, grasp the edges of the parchment paper and lift out the entire block. Place on a cutting board and use a large sharp knife to cut into 2-inch squares. Refrigerated in an airtight container, brownies will keep for up to 3 days.
Reprinted with permission from The Cookie Dough Lover's Cookbook, by Lindsay Landis, copyright (c) 2012. Published by Quirk Books.