01 - Preheat oven to 350°F. Grease a 9x13-inch baking pan and line with parchment paper.
02 - Whisk together flour, sugar, baking powder, baking soda, cocoa powder, and salt in a large bowl.
03 - Combine buttermilk, vegetable oil, eggs, vanilla extract, white vinegar, and red food coloring in a separate bowl. Mix well.
04 - Pour the wet ingredients into the dry ingredients. Mix just until combined—do not overmix.
05 - Pour the red velvet batter into the prepared pan and spread evenly with a spatula.
06 - Beat the softened cream cheese until smooth in a medium bowl. Add sugar, egg, and vanilla extract. 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.