Preheat your oven to 350°F (175°C) and grease a 9x13-inch baking pan.
In a medium saucepan, melt the butter over low heat.
Remove from heat and stir in the granulated sugar and brown sugar until combined.
Allow the mixture to cool slightly, then whisk in the eggs one at a time, followed by the vanilla extract.
In a separate bowl, sift together the flour, cocoa powder, baking powder, and salt.
Gradually add the dry ingredients to the wet mixture, stirring until just combined. Do not overmix.
Pour half of the brownie batter into the prepared baking pan and spread it evenly.
Drop spoonfuls of peanut butter over the batter, then pour the remaining brownie batter on top.
Use a knife or skewer to swirl the peanut butter into the brownie batter for a marbled effect.
If desired, sprinkle chocolate chips on top.
Bake in the preheated oven for 25-30 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs.
Allow the brownies to cool in the pan for at least 15 minutes before cutting into squares.