Preheat your oven to 350°F (175°C). Line an 8x8 inch baking pan with parchment paper, leaving overhang on two sides.
In a medium microwave-safe bowl, melt the butter in 30-second intervals. Stir in the sugar until combined.
Add eggs one at a time, whisking well after each addition. Stir in vanilla.
Add cocoa powder, flour, salt, and baking powder. Stir until just combined — do not overmix.
In a small bowl, stir together peanut butter, powdered sugar, and milk until smooth and pourable.
Pour brownie batter into the prepared pan and spread evenly.
Drop spoonfuls of peanut butter mixture over the top of the batter. Use a toothpick or butter knife to swirl it through in a figure-eight pattern.
Bake for 28–30 minutes, until the edges are set and the center has a slight jiggle.
Cool in the pan for at least 25–30 minutes before lifting out and slicing into 16 squares.
Notes
Store in an airtight container at room temperature for up to 4 days, or refrigerate for up to a week. These also freeze beautifully — wrap individual squares and freeze for up to 2 months.