Preheat your oven to 350°F (175°C). Grease a 9×9 inch baking pan or line it with parchment paper for easy removal.
In a large mixing bowl, combine the melted butter and granulated sugar. Stir until well combined. Add the eggs and vanilla extract, mixing until smooth.
In another bowl, whisk together the flour, cocoa powder, baking powder, and salt. Gradually add this dry mix to the wet ingredients, mixing until just combined. Add the red food coloring and mix until uniform.
In a separate bowl, use an electric mixer to beat the softened cream cheese until smooth. Add the sugar, egg, and vanilla extract and mix until creamy.
Pour half of the brownie batter into the prepared pan, spreading it evenly. Then, spoon the cheesecake batter over the brownie layer. Finally, add spoonfuls of the remaining brownie batter on top. Use a knife to swirl the layers together for a marbled effect.
Bake for 25-30 minutes or until the edges are set and a toothpick inserted in the center comes out with a few moist crumbs.
Allow the brownies to cool in the pan before cutting them into squares.