01 - Preheat the oven to 350°F. Grease and line a 9x13-inch baking pan with parchment paper.
02 - In a large bowl, whisk together flour, sugar, baking powder, baking soda, cocoa powder, and salt until well combined.
03 - In another bowl, combine buttermilk, oil, eggs, vanilla, vinegar, and red food coloring. Mix until fully incorporated.
04 - Pour the wet ingredients into the dry ingredients. Mix just until combined; do not overmix to maintain tender texture.
05 - In a medium bowl, beat the cream cheese until smooth. Add sugar, egg, and vanilla; mix until creamy and well-blended.
06 - Pour the red velvet batter into the prepared pan, spreading evenly. Dollop spoonfuls of cheesecake mixture over the batter. Use a knife or skewer to gently swirl for a marbled effect.
07 - Bake for 45–50 minutes, until a toothpick inserted into the center comes out clean. A small amount of cheesecake on the toothpick is acceptable.
08 - Cool completely in the pan on a wire rack before slicing and serving.