Preheat oven to 350 degrees and line a 9x9-inch baking pan with aluminum foil. Spray foil with cooking spray.
Mix brownie batter according to directions on box and spread evenly in prepared pan. Press peanut butter cups into batter so that batter comes almost all the way up the sides.
Place pan in oven and bake according to box directions. Let brownies cool.
To make peanut butter frosting, beat butter and peanut butter with an electric mixer until smooth. Beat in confectioners' sugar, milk, and vanilla pudding mix. Once smooth, spread on top of cooled brownies. Refrigerate at least 30 minutes.
Microwave heavy cream and butter in a microwave-safe bowl until starting to simmer. Add chocolate chips and stir until smooth. Let mixture cool. Place in a ziptop bag, snip the corner and drizzle on brownies.