Prepare the pan. Heat the oven to 350°F (175°C). Line an 8x8 inch pan with parchment paper, leaving some hanging over the sides so you can lift the brownies out later.
Mix the brownie batter. Whisk the melted butter and sugar together. Add the eggs and vanilla and whisk until smooth. Stir in the cocoa, flour, salt, and baking powder until just combined.
Bake. Spread the batter in the pan and bake for 22 to 25 minutes, until a toothpick comes out with a few moist crumbs. Do not overbake or the base will turn dry.
Cool completely. Let the brownies cool to room temperature. A warm base will melt the filling.
Make the peanut butter layer. Beat the softened butter and peanut butter until smooth. Add the powdered sugar, vanilla, and salt, and mix until thick and creamy.
Spread the filling. Press the peanut butter mixture evenly over the cooled brownies. Smooth the top with a spatula, and chill for 20 minutes.
Add the chocolate. Melt the chocolate chips and butter in 30-second bursts in the microwave, stirring each time, until smooth. Pour over the peanut butter layer and spread evenly.
Chill and slice. Refrigerate for 1 to 2 hours; 2 hours gives the cleanest slices. Lift the block out with the parchment and cut into 16 squares.