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, vinegar, and red food coloring until fully incorporated.
04 - Pour wet ingredients into dry ingredients. Stir gently until just combined, taking care not to overmix.
05 - Transfer red velvet batter to prepared pan, spreading evenly across the bottom using a spatula.
06 - Beat softened cream cheese until smooth. Add sugar, egg, and vanilla; mix until creamy and completely blended.
07 - Drop spoonfuls of cheesecake mixture randomly over red velvet batter. Use a knife or skewer to gently swirl through both batters, creating a marbled effect.
08 - Bake for 45 to 50 minutes, until toothpick inserted into center comes out clean (traces of cheesecake are acceptable).
09 - Allow cake to cool completely in pan on wire rack before slicing into squares.