Preheat the oven to 350°F (175°C). Lightly grease a 9x13-inch metal baking pan. Line the bottom with parchment paper, allowing excess to hang over the sides for easy removal. Grease the parchment as well.

In a medium saucepan over medium heat, melt the butter. Remove from heat and stir in the sugar until well combined. Add the eggs and vanilla extract, beating until fully incorporated. Mix in the cocoa powder, baking powder, and salt. Finally, fold in the flour until no dry streaks remain.

Transfer the brownie batter to the prepared pan and spread it evenly. Bake for 25–30 minutes, or until the center is set and a toothpick inserted comes out with moist crumbs. Allow the brownie layer to cool completely in the pan on a wire rack.

Using a stand mixer fitted with the paddle attachment, beat together the softened butter, peanut butter, and powdered sugar until smooth. Gradually add milk, one teaspoon at a time, until the mixture reaches a spreadable consistency. Evenly spread the filling over the cooled brownies. Refrigerate for 30 minutes to set.

In a microwave-safe bowl or double boiler, combine the peanut butter, chocolate chips, butter, and cream. Heat gently until melted, stirring until smooth. Pour the ganache over the peanut butter layer and spread evenly. Return the pan to the refrigerator until the ganache is fully set.

Once the ganache has firmed up, lift the brownies out using the parchment handles. Cut into bars or squares using a sharp knife. Wipe the blade clean between slices for neater edges.