Creating Red Velvet Cheesecake Brownies is straightforward if you follow these steps:

1. Preheat Oven: Preheat your oven to 350°F (175°C). Grease a 9×13 inch baking pan or line it with parchment paper for easy removal.
2. Prepare the Brownie Mixture: In a medium saucepan, melt the unsalted butter over low heat. Once melted, remove it from the heat and stir in the sugar until well combined.
3. Add Eggs and Vanilla: Whisk in the eggs, one at a time, followed by the vanilla extract. Mix until smooth and glossy.
4. Combine Dry Ingredients: In a separate bowl, whisk together the flour, cocoa powder, baking powder, and salt.
5. Combine Wet and Dry: Gradually add the dry ingredients to the wet mixture, stirring until just combined. Mix in the red food coloring until you achieve a uniform color.
6. Prepare the Cheesecake Layer: In another bowl, beat the softened cream cheese with sugar until creamy. Add the egg and vanilla extract, mixing until smooth and well incorporated.
7. Layer the Mixtures: Pour half of the brownie batter into the prepared baking pan. Spread evenly. Spoon the cheesecake mixture over the brownie layer, spreading it gently. Finally, top with the remaining brownie batter, dolloping it over the cheesecake layer.
8. Swirl the Mixtures: Use a knife or skewer to gently swirl the brownie and cheesecake layers together for a marbled effect.
9. Bake: Place the pan in the preheated oven and bake for 30-35 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs.
10. Cool: Remove from the oven and allow to cool in the pan for 15-20 minutes. Then, transfer to a wire rack to cool completely before cutting into squares.

With these steps, you’ll have a batch of Red Velvet Cheesecake Brownies that will impress everyone!