Preheat the oven to 350°F (175°C). In a medium bowl, whisk together the flour, cocoa powder, baking powder, baking soda, and salt. In a large mixing bowl, combine sugar, vegetable oil, buttermilk, eggs, food coloring, vanilla extract, and vinegar. Gradually add dry ingredients to wet mixture, stirring until smooth.

Divide the batter between two greased 9-inch round cake pans. Bake for 25-30 minutes or until a toothpick comes out clean. Cool in pans for 10 minutes, then turn out onto wire racks to cool completely.

For the cheesecake layer, preheat the oven to 325°F (163°C). Beat cream cheese and sugar until creamy. Add sour cream, eggs, and vanilla until fully integrated. Pour into a greased springform pan and bake for 45-50 minutes until edges are set.

Once the layers have cooled completely, place one red velvet cake layer on a platter, top with the cheesecake layer, then add the second red velvet layer.

For the frosting, beat together softened butter, cream cheese, and vanilla until light. Gradually mix in powdered sugar until smooth, adding milk if needed for consistency.

Frost the top and sides of the cheesecake and refrigerate for at least 4 hours or overnight before serving.