Preheat your oven to 350°F (175°C). Grease a 9x13 inch baking pan or line it with parchment paper for easy removal.

In a medium saucepan, melt the butter over low heat. Once melted, remove from heat and stir in granulated sugar. Let it cool slightly.

Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

In a separate bowl, whisk 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.

In a medium bowl, combine the creamy peanut butter, powdered sugar, milk, and ½ teaspoon of vanilla extract. Mix until well combined and smooth.

Spread the peanut butter mixture evenly over the brownie layer in the pan.

Pour the remaining brownie batter over the peanut butter layer and spread it out gently to cover.

Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.

Remove from the oven and allow the brownies to cool in the pan on a wire rack. Once cooled, cut into squares and serve.