Preheat the oven to 350°F (175°C). Cheesecake
Prepare a 9-inch springform pan: spray with non-stick spray (with flour), wrap the bottom of the pan with heavy-duty foil so water cannot seep in, and set the pan aside. Bring water to a boil for the water bath and have it hot when ready to use.
In a large bowl, beat 32 ounces cream cheese (room temperature) and 1 cup granulated sugar together on medium speed until smooth and fluffy, scraping down the sides of the bowl as needed.
Add the 4 large eggs (room temperature) one at a time, beating after each addition until just incorporated.
Beat in 3/4 cup sour cream (room temperature) and 1 tablespoon vanilla extract until smooth.
Pour the cheesecake batter into the prepared springform pan. Place the springform pan inside a larger roasting pan or baking pan with high sides. Carefully pour the hot water into the outer pan until it comes about halfway up the sides of the springform pan.
Bake the cheesecake at 350°F for 45–55 minutes, or until the edges are set and the center still has a slight wobble (it should not be liquid).
Turn off the oven and leave the cheesecake inside the closed oven for 1 hour to finish gently cooking.
Remove the springform pan from the water bath, peel away the foil, and place the pan on a cooling rack. Let the cheesecake cool to room temperature, then refrigerate until fully chilled (best if left overnight). Red Velvet Cake
Prepare two 9-inch cake pans: grease the pans, line the bottoms with parchment paper, and spray with non-stick cooking spray with flour.
In a medium bowl, sift together 2 1/2 cups cake flour, 1 teaspoon baking soda, 1 teaspoon salt, and 1/4 cup plus 2 tablespoons unsweetened cocoa powder. Set aside.
In the bowl of a stand mixer (or a large bowl with a hand mixer), cream 1 cup unsalted butter (room temperature) and 1 1/2 cups granulated sugar on medium speed until light and fluffy, about 2–3 minutes.
Add the 2 large eggs one at a time, mixing until each is incorporated.
Add 1 cup buttermilk, 4 tablespoons red food coloring, 2 teaspoons vanilla extract, and 1 tablespoon distilled white vinegar. Mix until combined.
With the mixer on low, add the dry ingredients to the wet ingredients and mix just until the batter is smooth and homogeneous. Do not overmix.
Divide the batter evenly between the two prepared 9-inch pans and smooth the tops.
Bake at 350°F for about 25 minutes, or until a toothpick inserted into the center comes out clean.
Let the cakes cool in the pans for 5–10 minutes, then invert or lift them out onto a cooling rack, remove the parchment, and cool completely before frosting. Frosting
In a large bowl, beat 1 cup unsalted butter (room temperature), 8 ounces cream cheese (room temperature), and 2 teaspoons vanilla extract together until smooth and creamy.
Gradually add 3 1/2 cups sifted powdered sugar and continue beating until the frosting is light and fluffy, about 4–5 minutes. If using, add 2 tablespoons cream of coconut and mix until blended. Keep the frosting chilled if the kitchen is warm. Assemble Cake
If the red velvet cakes have domed tops, level them with a serrated knife so they are flat.
Place one red velvet cake layer on a serving plate or cake board. Spread a thin, even layer of frosting over the top of that cake layer.
Remove the chilled cheesecake from the springform pan: run a thin knife around the edge to loosen, unlatch and remove the ring, then lift the cheesecake off the base (or slide the base out and transfer the cheesecake carefully). Place the cheesecake (still chilled) on top of the frosted first red velvet layer, centered.
Spread a thin layer of frosting over the top of the cheesecake.
Place the second red velvet cake layer on top of the cheesecake, pressing gently to level.
Use the remaining frosting to crumb-coat and then fully frost the top and sides of the assembled cake. Decorate with sprinkles or shaved white chocolate if desired.
Refrigerate the finished cake until ready to serve to help the layers set (serve chilled or bring to slightly cooler-than-room temperature before slicing for cleaner cuts).