Preheat your oven to 350°F (175°C).
Prepare an 8x8-inch baking pan by greasing it or lining it with parchment paper.
In a large mixing bowl, sift together the cocoa powder, baking powder, and salt.
In another bowl, mix the creamy peanut butter and granulated sugar until well blended. Add the eggs and vanilla extract, stirring until smooth.
Gradually add the dry mixture to the wet mixture, stirring gently until combined.
If desired, add a peanut butter swirl by dropping spoonfuls of peanut butter on top of the batter and swirling with a knife.
Pour the brownie batter into the prepared baking pan and spread evenly. Bake for 20-25 minutes.
Let the brownies cool in the pan for about 10 minutes, then transfer to a wire rack to cool completely before cutting into squares.