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, mix buttermilk, vegetable oil, eggs, vanilla extract, white vinegar, and red food coloring until smooth.
04 - Pour wet ingredients into dry ingredients. Stir gently until just combined, being careful not to overmix.
05 - Beat softened cream cheese until smooth. Add sugar, egg, and vanilla extract. Mix until creamy and fully blended.
06 - Spread red velvet batter evenly in prepared pan. Drop spoonfuls of cheesecake mixture over batter. Use knife to gently swirl for marbled effect.
07 - Bake for 45-50 minutes until toothpick inserted in center comes out clean. Slight cheesecake residue on toothpick is acceptable.
08 - Cool completely in pan on wire rack before slicing. Serve chilled or at room temperature.