Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large bowl, whisk together melted butter and sugar until smooth.
Add eggs and vanilla extract; mix until well combined.
Sift in the cocoa powder, flour, baking powder, and salt. Stir until a thick dough forms.
Scoop tablespoon-sized portions of dough onto the baking sheet.
Add a small dollop of peanut butter on top of each dough ball and swirl with a knife or toothpick.
Bake for 10–12 minutes, or until edges are set.
Cool on the baking sheet for a few minutes before transferring to a wire rack.