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 evenly distributed.
03 - In another bowl, combine buttermilk, oil, eggs, vanilla, vinegar, and red food coloring. Whisk until well blended.
04 - Pour the wet ingredients into the dry ingredients. Mix gently until just combined; do not overmix to maintain tender texture.
05 - Pour the red velvet batter into the prepared pan, spreading evenly across the bottom with a spatula.
06 - In a medium bowl, beat the cream cheese until smooth. Add sugar, egg, and vanilla; mix until creamy and fully blended.
07 - Dollop spoonfuls of the cheesecake mixture over the red velvet batter. Use a knife or skewer to gently swirl the cheesecake into the batter for a marbled effect.
08 - Bake for 45 to 50 minutes, or until a toothpick inserted into the center comes out clean. A small amount of cheesecake on the toothpick is acceptable.
09 - Cool completely in the pan on a wire rack before slicing and serving to ensure clean cuts and proper texture.