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, oil, eggs, vanilla, vinegar, and red food coloring in a separate bowl. Mix thoroughly.
04 - Pour wet ingredients into dry ingredients. Stir until just combined; avoid overmixing to prevent dense texture.
05 - Spread red velvet batter evenly into prepared pan using a spatula.
06 - Beat cream cheese until smooth. Add sugar, egg, and vanilla; mix until creamy and well-blended.
07 - Drop spoonfuls of cheesecake mixture over batter. Use knife or skewer to gently swirl for marbled pattern.
08 - Bake for 45–50 minutes until toothpick inserted in center comes out clean. Slight cheesecake residue is acceptable.
09 - Cool completely in pan on wire rack before slicing and serving.