Place rack in the center of the oven and preheat oven to 350°F Lightly grease the bottoms of three 9-inch round cake pans with shortening, then dust with flour. Shake out excess flour and set the pans aside. An easier method: place cake pan on a piece of wax paper. Trace the bottom and cut with sizzors to fit into bottom of pan. Repeat for remaining cake pans. No need to grease. I promise the cake will fall out after running a knife around the sides.
Place the cake mix, cocoa powder, buttermilk, food coloring, melted butter, eggs, vanilla, baking soda and vinegar in a large mixing bowl and beat with an electric mixer on low speed until ingredients are incorporated, 1 minute. Stop machine and scrape down side of bowl with rubber spatula. Increase the mixer speed to medium and beat for 2 minutes longer, scraping the side of the bowl again if needed. The batter should look well-blended. Divide batter evenly among three prepared pans, about 1 ½ cups batter per pan, smoothing the tops with rubber spatula. Place pans in the oven. If your oven is not large enough to hold three pans on center rack, place two on that rack and one in the center of the rack above.
Bake cake layers until they just start to pull away from the sides of the pans and the tops spring back when lightly pressed with a finger, 17 to 21 minutes. The layer on the higher rack may bake faster so test it for doneness first.
Transfer cake pans to wire racks and cool for 5 minutes. Run a dinner knife around the edge of each layer and give the pans a good shake to loosen cakes. Invert each layer onto a wire rack. At this point if you've used wax paper, remove the paper and discard then invert it again onto another rack so the cakes are right side up. Let the layers cool completely. Make frosting.
To assemble the cake, transfer one cake layer, right side up, to a serving platter. Spread the top with some of the frosting. Place a second cake layer, right side up, on top of the first and frost the top. Repeat this process with the third layer. Frost the side of the cake with a thin coat just to set the crumbs. Use the remaining frosting to go back over this and liberally frost the side, working with smooth, clean strokes. To make slicing easier, place uncovered cake in the refrigerator until frosting sets, 20 minutes.
Cream Cheese Frosting:
Place cream cheese and room-temperature butter in a large mixing bowl and beat with an electric mixer on high speed until light and fluffy, 1 to 2 minutes. Stop machine and scrape down side of bowl with rubber spatula. Add vanilla extract and 4 cups sifted powdered sugar; beat on medium speed until well combined. Increase the mixer speed to high and beat the frosting for 1 minute longer.