Preheat your oven to 350°F (175°C). Grease and line the bottom of two 6-inch round cake pans.
In a medium bowl, sift together the flour, sugar, cocoa powder, baking soda, and salt.
In another bowl, whisk together the buttermilk, oil, egg, red food coloring, vanilla extract, and vinegar.
Gradually mix the dry ingredients into the wet ingredients until smooth.
Divide the batter evenly between the two pans and bake for 20-25 minutes or until a toothpick comes out clean. Let the cakes cool in the pans for 10 minutes, then move them to a wire rack to cool completely.
Preheat the oven to 325°F (163°C). Line the bottom of a 6-inch springform pan and wrap the outside with foil.
In a bowl, beat the cream cheese and sugar until smooth. Add the eggs one at a time, mixing well after each addition. Then, mix in the vanilla and sour cream.
Pour the cheesecake batter into the prepared pan. Place this pan inside a larger pan and fill it with hot water halfway up the sides (this is called a water bath).
Bake for 45-50 minutes or until the center is set. Turn off the oven and leave the cheesecake in the oven with the door slightly open for 1 hour. After that, refrigerate for at least 4 hours.
Once the red velvet cakes and cheesecake are fully cooled, place one red velvet layer on a serving plate.
Top with the cheesecake layer, then add the second red velvet layer on top.