Preheat your oven to 350°F (175°C). Line an 8x8-inch baking pan with parchment paper, leaving an overhang on two sides to easily lift the brownies out later. Lightly grease the paper and any exposed sides of the pan.

In a large mixing bowl, whisk together the melted butter and granulated sugar until well combined. Add the eggs one at a time, whisking well after each addition until the mixture is glossy. Stir in the vanilla extract.

In a separate medium bowl, whisk together the all-purpose flour, sifted cocoa powder, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, mixing with a spatula until just combined. Do not overmix.

Gently fold in the semi-sweet chocolate chips. Pour the brownie batter into the prepared pan and spread evenly with the spatula.

In a medium bowl, combine the creamy peanut butter, powdered sugar, 2 tablespoons of melted butter, and 1/2 teaspoon of vanilla extract. Stir until the mixture is smooth and creamy. If it's too thick to dollop, you can microwave it for 10-15 seconds to soften it slightly.

Drop spoonfuls of the peanut butter mixture evenly over the top of the brownie batter.

Using a butter knife or a skewer, gently swirl the peanut butter into the brownie batter to create a marbled effect. Be careful not to over-mix, as you want distinct swirls.

Bake for 28-32 minutes, or until a toothpick inserted into the center comes out with moist, fudgy crumbs attached (not wet batter). The edges should look set.

Remove the pan from the oven and place it on a wire rack. Let the brownies cool completely in the pan for at least 2 hours before lifting them out with the parchment paper overhang and cutting into 16 squares. This cooling period is crucial for achieving a chewy texture and clean cuts.