01 - Preheat oven to 325°F. Grease a 9-inch springform pan thoroughly and line the bottom with parchment paper to prevent sticking.
02 - Whisk together flour, cocoa powder, baking soda, and salt in a medium bowl until evenly combined.
03 - Beat sugar, oil, and egg in a separate bowl until light and fluffy. Mix in buttermilk, vinegar, vanilla extract, and red food coloring until uniform in color.
04 - Gradually add dry ingredients to wet mixture, folding gently until just incorporated. Pour batter into prepared pan and spread into an even layer.
05 - Bake for 15 minutes until slightly set. The center will appear underdone, which is expected as it will continue cooking with the cheesecake layer.
06 - Beat cream cheese and sugar until completely smooth and creamy. Add eggs one at a time, mixing thoroughly after each addition. Incorporate sour cream, vanilla, and flour until just combined.
07 - Pour cheesecake batter over the partially baked cake layer. Smooth the surface with an offset spatula. Bake for 1 hour 5 minutes until the center is set with a slight wobble.
08 - Turn off oven and crack the door open. Allow cheesecake to cool inside for 1 hour to prevent cracking. Remove and cool completely to room temperature.
09 - Refrigerate for at least 6 hours or overnight until fully set and cold throughout.
10 - Beat cream cheese and butter until fluffy and light. Add powdered sugar and vanilla, continuing to beat until smooth and spreadable.
11 - Release springform ring carefully. Frost if desired and slice into 12 portions. Serve chilled.