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 large mixing bowl, combine the melted butter, granulated sugar, and brown sugar. Mix until well combined.
Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
In another bowl, whisk together the flour, cocoa powder, salt, and baking powder. Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Pour half of the brownie batter into the prepared baking pan, spreading it evenly.
In a separate bowl, beat the softened cream cheese with the granulated sugar until smooth. Add the egg and vanilla extract, mixing until well combined. Spread the cheesecake mixture over the brownie layer in the pan.
Spoon the remaining brownie batter on top of the cheesecake layer. Use a knife or toothpick to swirl the two layers together for a marbled effect.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Allow to cool in the pan for about 15 minutes, then transfer to a wire rack to cool completely before slicing.