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 - In a separate bowl, combine buttermilk, oil, eggs, vanilla, vinegar, and red food coloring. Mix well.
04 - Pour wet ingredients into dry ingredients. Mix just until combined. Do not overmix.
05 - Pour red velvet batter into prepared pan, spreading evenly with a spatula.
06 - Beat cream cheese until smooth in a medium bowl. Add sugar, egg, and vanilla. Mix until creamy and well-blended.
07 - Dollop spoonfuls of cheesecake mixture over red velvet batter. Use a knife or skewer to gently swirl for a marbled effect.
08 - Bake for 45-50 minutes 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.