Preheat your oven to 350°F (175°C). Grease a 9x9 inch baking pan.
In a mixing bowl, combine the melted butter and sugar. Add the eggs and vanilla extract, and whisk until smooth.
Stir in the cocoa powder, flour, salt, and baking powder until just combined.
Pour the batter into the prepared baking pan.
In a small bowl, mix the peanut butter and powdered sugar until smooth. Drop spoonfuls of the peanut butter mixture onto the brownie batter. Use a knife to swirl the peanut butter into the batter.
Bake for 30 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs. Let cool before cutting into squares.