Preheat the oven to 350°F (177°C). Spray two 8-inch cake pans with baking spray, line the bottoms with parchment rounds cut to fit, then spray the parchment. Set pans aside.
In a medium bowl whisk together the dry cake ingredients: 2 1/2 cups all-purpose flour, 1 1/2 cups sugar, 1 teaspoon baking soda, 1 teaspoon baking powder, 1/2 teaspoon salt, and 1/3 cup cocoa powder. Set aside.
In a large bowl combine the wet cake ingredients: 2 large eggs (room temperature), 1 1/2 cups vegetable oil, 1 cup buttermilk (room temperature), 1 teaspoon white distilled vinegar, 1 teaspoon vanilla extract, and 1 teaspoon red gel food coloring (or 2 tablespoons regular food coloring). Using a hand mixer or stand mixer, beat on medium speed until evenly combined.
Reduce mixer speed to low and gradually add the dry ingredients to the wet ingredients. Stop occasionally to scrape the sides and bottom of the bowl. Mix only until the batter is thoroughly combined; do not overmix.
Divide the cake batter evenly between the two prepared pans and smooth the tops. Bake, rotating the pans halfway through, until a toothpick inserted in the center comes out clean, about 30 minutes.
Remove the pans from the oven. Run a knife around the edges to loosen the cakes and let them cool in the pans for 20–30 minutes. Invert each cake onto a plate, then re-invert onto a cooling rack with the round (domed) side up. Cool completely before assembling.
While the cakes cool, prepare the oven and pans for the cheesecakes: preheat the oven to 325°F (163°C). Spray two 8-inch cake pans with baking spray and line the bottoms with parchment rounds. Set aside.
In a large bowl beat 24 ounces cream cheese (softened to room temperature) on medium for about 1 minute until smooth.
Add 1 cup granulated sugar and 2 tablespoons all-purpose flour to the cream cheese. Mix until combined and there are no lumps, scraping down the sides of the bowl as needed.
With the mixer on low, add the 2 large eggs (room temperature) one at a time, mixing until each egg is just incorporated. Scrape the bowl as needed and avoid overbeating.
Add 1/2 tablespoon vanilla extract, 1 cup sour cream (room temperature), and 1/2 teaspoon salt. Beat on low until just combined, stopping to scrape the sides and bottom of the bowl.
Divide the cheesecake batter evenly between the two prepared pans and level the tops with a spatula.
Bake the cheesecakes 40–45 minutes, until the centers are just slightly wobbly while the edges are set and puffed.
Turn the oven off and crack the oven door open. Allow the cheesecakes to cool completely inside the oven with the door ajar.
Once fully cooled, refrigerate the cheesecakes (in their pans) for at least 5–6 hours or overnight. When ready to use, run a butter knife around the edge to release each cheesecake from its pan and keep refrigerated until assembly.
Prepare the Cream Cheese Frosting following the recipe instructions on the blog.
Before assembling, level the two red velvet cake layers and the two cheesecake layers with a cake leveler or a sharp serrated knife so they are flat and even.
Place a cake board or cake stand on your work surface. Spread a small amount of frosting onto the board to anchor the cake.
Assemble the cake from bottom to top as follows: place one red velvet cake layer (flat side down) on the board, spread an even layer of frosting over it, place one cheesecake layer on top, spread another even layer of frosting, place the second red velvet cake layer, spread an even layer of frosting, and finish by placing the second cheesecake layer on top.
Use the remaining frosting to apply a thin crumb coat over the entire cake. Chill the cake briefly (15–30 minutes) to set the crumb coat, then apply a final smooth layer of frosting to the top and sides.
Press cake crumbs onto the sides/edges if desired. Refrigerate the assembled cake for at least 4 hours (longer is better) to allow the frosting to set before slicing.
Serve chilled. Optionally serve with whipped cream on the side.