Preheat your oven to 350°F (175°C). Line a 9x9-inch baking pan with parchment paper, leaving an overhang on the sides.
Make the brownie base: In a saucepan over low heat, melt the butter and chopped chocolate together, stirring until smooth. Let cool slightly.
Whisk in the sugars, then add the eggs one at a time, beating well after each addition. Stir in the vanilla.
Sift together the flour, cocoa powder, and salt. Fold into the chocolate mixture just until combined.
Pour the batter into the prepared pan and smooth the top. Bake for 25 minutes, or until a toothpick inserted comes out with a few moist crumbs.
Cool completely in the pan on a wire rack.
Make the cookie dough topping: In a large bowl, cream together the butter and both sugars until light and fluffy. Add milk and vanilla, beating until smooth.
Add the heat-treated flour and salt, mixing until incorporated. Fold in the chocolate chips.
Spread the cookie dough evenly over the cooled brownies. Chill for at least 1 hour before slicing.
Cut into 16 squares and serve cold or at room temperature.