Preheat oven to 350°F (175°C) and grease an 8x8 inch baking pan.
In a medium bowl, whisk 1/2 cup melted butter and granulated sugar until well combined.
Beat in the eggs and vanilla extract until the mixture is smooth.
Gently fold in cocoa powder, all-purpose flour, salt, and baking powder until no dry streaks remain.
In a separate small bowl, stir together creamy peanut butter, powdered sugar, and 2 tablespoons melted butter until smooth.
Spread the chocolate batter evenly into the prepared baking pan.
Dollop the peanut butter mixture over the chocolate batter and use a knife to create a marble swirl pattern.
Bake for 25 to 30 minutes until a toothpick inserted into the center comes out with a few moist crumbs.
Remove from oven and allow to cool completely in the pan before slicing into 16 squares.