Preheat your oven to 350°F (175°C). Grease your 9x13-inch baking pan lightly with butter or line it with parchment paper for easy removal.
In a large bowl, combine the melted unsalted butter and granulated sugar. Whisk until well blended. Add the eggs one at a time, mixing thoroughly after each addition. Stir in the teaspoon of vanilla extract.
In a separate bowl, sift together the all-purpose flour, cocoa powder, baking powder, and salt. Gradually fold the dry ingredients into the wet mixture until just combined—be careful not to overmix to keep the brownies tender.
Using a mixer, beat the softened cream cheese until smooth and creamy. Add the creamy peanut butter, powdered sugar, and vanilla extract. Continue mixing until the filling is silky and well combined with no lumps.
Pour half of the brownie batter into the prepared pan and spread it evenly. Dollop the peanut butter cheesecake mixture on top, then gently spread it with a spatula, taking care not to mix it completely with the brownie layer.
Top with the remaining brownie batter and scatter the chocolate chips evenly over the surface.
Using a knife or a skewer, swirl the brownie and cheesecake layers together gently to create a marbled effect.
Place the pan in the oven and bake for 35-40 minutes, or until a toothpick inserted near the center comes out with a few moist crumbs but not wet batter.
Allow the brownies to cool completely in the pan on a cooling rack. Once cooled, cut into squares and enjoy.