Preheat oven to 325 degrees F. Grease a 9x13 inch pan. Line pan with parchment paper. Set aside.
In a medium microwaveable bowl, melt chocolate in the microwave at 30 second intervals on half power until chocolate is melted and smooth. Stir after each intervals to ensure even melting. Set aside to slightly cool.
In a large mixing bowl, whisk together melted butter and brown sugars. Add the eggs one at a time and whisk until combined. Add in cooled melted chocolate. Fold in the flour and mix until just incorporated.
Spread batter into prepared pan. Bake for 25-30 minutes until toothpick inserted in the center of brownie comes out clean. Let cool in pan.
Prepare cookie dough while waiting for brownies to cool. In the bowl of a stand mixer, cream together butter, peanut butter, brown sugar, granulated sugar, and salt. Add in milk and vanilla. Stir in flour just until combined.
Spread the cookie dough over the cooled brownies in a nice even layer. Sprinkle chopped peanut butter cups on top. Slightly press toppings into the cookie dough layer. Refrigerate completed cookie dough brownie until firm to the touch. You can also place it in the freezer if you want to speed up the process. The colder and firmer the dough, the easier it will be to cut later.