01 - Preheat the oven to 350°F. Grease a 9x13-inch baking pan and line 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, whisk buttermilk, vegetable oil, eggs, vanilla extract, white vinegar, and red food coloring until smooth.
04 - Pour the wet ingredients into the dry ingredients. Mix gently until just combined, being careful not to overmix.
05 - Pour the red velvet batter into the prepared pan and spread evenly with a spatula.
06 - In a medium bowl, beat cream cheese until smooth. Add sugar, egg, and vanilla; mix until creamy and well-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 45-50 minutes, or until a toothpick inserted into the center comes out clean. A little cheesecake on the toothpick is acceptable.
09 - Cool completely in the pan on a wire rack before slicing and serving.