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.