Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans; line the bottoms with parchment paper.

In a mixing bowl, combine the flour, baking powder, baking soda, salt, and cocoa powder. Set aside.

In a separate bowl, using an electric mixer, beat together the vegetable oil and sugar until well combined. Add the buttermilk, eggs, food coloring, vanilla extract, and vinegar, mixing until smooth.

Gradually add the dry ingredients to the wet mixture, mixing until just combined. Do not overmix.

Divide the red velvet cake batter evenly between the prepared cake pans. Bake in the preheated oven for 25-30 minutes, or until a toothpick inserted in the center comes out clean. Remove from the oven and cool in the pans for 10 minutes, then transfer to a cooling rack to cool completely.

While the cakes are cooling, make the cheesecake layer. In a mixing bowl, beat the softened cream cheese and sugar together until smooth. Add the eggs, one at a time, mixing well after each addition. Stir in the vanilla extract and sour cream until fully combined.

Reduce the oven temperature to 325°F (160°C). Pour the cheesecake batter into a greased 9-inch round cake pan. Bake for about 50-60 minutes or until the edges are set but the center is still slightly jiggly. Turn off the oven and let the cheesecake cool inside with the door slightly ajar for about an hour. Remove from the oven and cool completely.

Once the red velvet cakes and the cheesecake layer are completely cooled, assemble the cake. Place one layer of red velvet cake on a serving platter, top with the cheesecake layer, then add the second layer of red velvet cake on top.

Optional: Frost the cake with cream cheese frosting and decorate as desired.