Preheat your oven to 350°F (175°C) and grease an 8x8-inch baking pan, lining it with parchment paper for easy removal.

In a large mixing bowl, combine melted butter and 1 cup of granulated sugar, whisking until smooth. Add 2 eggs and 1 teaspoon of vanilla extract, mixing well.

In a separate bowl, whisk together flour, cocoa powder, baking powder, and salt. Gradually add the dry ingredients to the wet mixture, stirring until just combined. Add red food coloring and mix until evenly colored.

In a medium bowl, beat softened cream cheese with 1/4 cup of granulated sugar until smooth. Add 1 egg and 1 teaspoon of vanilla extract, mixing until fully incorporated.

Pour half of the brownie batter into the prepared pan, spreading it evenly. Spoon the cheesecake mixture over the brownie layer, spreading it gently to cover.

Drop spoonfuls of the remaining brownie batter on top of the cheesecake layer. Use a knife or toothpick to swirl the two layers together, creating a marbled effect.

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

Allow the brownies to cool in the pan for at least 15 minutes before lifting them out using the parchment paper. Let them cool completely on a wire rack before slicing.