01 - Preheat 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 a separate bowl, whisk buttermilk, vegetable oil, eggs, vanilla extract, white vinegar, and red food coloring until fully incorporated.
04 - Pour wet ingredients into dry ingredients. Mix gently until just combined, taking care not to overmix.
05 - Transfer red velvet batter to prepared pan, spreading evenly across the surface with a spatula.
06 - Beat softened cream cheese until smooth and creamy. Add sugar, egg, and vanilla extract; mix until well blended and lump-free.
07 - Dollop spoonfuls of cheesecake mixture over the red velvet batter. Use a knife or skewer to gently swirl through the batter, creating a marbled pattern.
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 - Let cake cool completely in the pan on a wire rack before slicing and serving.