Creating Red Velvet Cheesecake Brownies is a simple process that yields stunning results. Follow these steps:

1. Preheat Oven: Preheat your oven to 350°F (175°C). Grease and line a 9×13-inch baking pan with parchment paper for easy removal.
2. Melt Butter: In a saucepan over low heat, melt the unsalted butter completely. Remove from heat and allow it to cool slightly.
3. Mix Wet Ingredients: In a large bowl, whisk together the melted butter and granulated sugar until well combined. Add in the eggs, one at a time, followed by the vanilla extract. Mix until smooth.
4. Combine Dry Ingredients: In another bowl, sift together the flour, cocoa powder, baking powder, and salt.
5. Combine Mixtures: Gradually add the dry ingredients to the wet mixture, stirring until smooth. Once mixed, add the red food coloring until fully incorporated.
6. Prepare Cheesecake Mixture: In a separate bowl, beat the softened cream cheese and powdered sugar until creamy and smooth. Then add the egg yolk and mix until combined.
7. Layer Brownie Batter: Pour half of the brownie batter into the prepared pan, spreading it evenly.
8. Add Cheesecake Layer: Dollop the cheesecake mixture over the brownie batter and use a spatula to spread it gently.
9. Top with Remaining Batter: Pour the remaining brownie batter on top of the cheesecake layer. Use a knife to swirl the two mixtures together for a marbled effect.
10. Bake: Bake for 30-35 minutes or until a toothpick inserted in the center comes out clean or with a few moist crumbs.
11. Cool: Remove from the oven and allow the brownies to cool in the pan for 15-20 minutes. Then, lift the brownies out using the parchment paper and let them cool fully on a wire rack.

These steps will guide you through the baking process, ensuring that your brownies come out perfectly every time!