Make the Cheesecake: Preheat oven to 350 degrees F. Spray a 9-inch springform pan with non-stick cooking spray and line the bottom with a round of parchment paper.
Using an electric mixer on medium-low speed, beat the cream cheese, sugar, flour, and salt until the mixture is creamy and no lumps of cream cheese remain, about 3 minutes. Scrape down the sides of the bowl, add the heavy cream and vanilla, and beat to combine. Beat in the eggs one at a time, beating for about 15 seconds before adding the next. Using a rubber spatula, mix a few times by hand to ensure that all of the ingredients are evenly incorporated.
Pour the filling into the prepared pan and spread into an even layer. Bake until the cheesecake is set and does not jiggle, about 40 to 55 minutes. Remove from the oven and cool on a wire rack for at least 1 hour. Once the cheesecake has cooled to room temperature, place it in the freezer for at least 3 hours or overnight.
Make the Red Velvet Cake: Preheat oven to 350 degrees F. Grease two 9-inch cake pans. Line the bottoms of the pans with a parchment round, butter the parchment paper, and then flour the pans.
On medium-high speed, cream the butter and sugar until light and fluffy, about 3 minutes. Turn the mixer to high and add the eggs one at a time, mixing for about a minute after each addition. Scrape down the bowl and beat until well incorporated.
In a separate small bowl, mix together the cocoa powder, vanilla extract and red food coloring to make a thick paste. Add to the batter and mix on medium speed until completely combined. You may need to stop the mixer to scrape the bottom of the bowl, making sure that all the batter gets color.
Reduce the mixer speed to low and slowly add half of the buttermilk. Add half of the flour and mix until combined. Scrape the bowl and repeat the process with the remaining buttermilk and flour. Beat on high until smooth.
Again, reduce the mixer speed to low and add the salt, baking soda and vinegar. Turn to high and beat for another couple of minutes until completely combined and smooth.
Divide the batter evenly between the two cake pans and bake for about 30 minutes, or until a thin knife or skewer inserted into the center comes out clean. Cool for 10 minutes and then remove cakes from the pans and place them on a cooling rack to cool completely.
Make the Frosting: Using an electric mixer, beat the butter, powdered sugar, vanilla, and salt on low speed until smooth, then mix for an additional 2 minutes, scraping down the bowl as needed. Increase the speed to medium-low and add the cream cheese one piece at a time and mix until smooth, then mix for an additional 2 minutes.
Assemble the Red Velvet Cheesecake: Level the tops of the cakes if necessary, then place one cake layer on a serving platter. Remove the cheesecake from the freezer and remove the sides of the springform pan. Slide a knife between the bottom of the cheesecake and the parchment paper to remove the cheesecake from the pan bottom and parchment round. If the cheesecake is wider than the cake layers, use a sharp knife to gently shave off some of the sides of the cheesecake so it is the same width as the cake layers.
Place the cheesecake layer on top of the first cake layer, then place the second cake layer on top of the cheesecake layer, upside-down.
Spread a very thin layer of cream cheese frosting (the “crumb coat”) over the top and sides of the cake, then refrigerate for 30 minutes to set the frosting. Then apply another liberal coat of frosting and decorate as desired. Keep refrigerated, then let sit at room temperature for 20 minutes before serving. Cover leftovers and store in the refrigerator for up to 5 days.