Preheat the oven to 350°F (180°C). Grease a 8x8-inch pan and line it with parchment paper, leaving an overhang on the sides to lift the finished bars out. Set aside.
Place butter and chocolate in a heatproof bowl over a saucepan of simmering water (don't let the bowl touch the water). Stir until melted then remove from heat.
Quickly stir in sugar, flour, cocoa powder, eggs, vanilla extract and salt until just combined. Pour batter into prepared pan.
Bake for 30 minutes or until a skewer inserted in the center comes out with only with a few moist crumbs attached. Set aside to cool completely, about 1 hour.
In the bowl of a stand mixer fitted with the paddle attachment, beat cream cheese, peanut butter, powdered sugar and vanilla together on medium speed until smooth and creamy. Spread evenly onto crust. Set aside.
Place butter and chocolate in a heatproof bowl over a saucepan of simmering water (don't let the bowl touch the water). Stir until melted and smooth. Spread evenly over peanut butter filling. Refrigerate until set, for about 2 hours.
Use the parchment paper to lift the bars from the pan and cut into small pieces. Store bars covered in the refrigerator.