Make the Red Velvet Cake. Preheat the oven to 350F and grease 3 8-inch round cake pans and line with parchment paper to ensure the batter doesn't stick. Set aside.
In a large mixing bowl, sift and whisk together the cake flour, cocoa powder, espresso powder, baking soda, baking powder, and salt. Set aside.
Beat the butter, oil, and sugar with a mixer on medium-high speed until smooth and creamy, about 2 minutes. Then, mix in sour cream, vinegar, egg yolks (not the whites, which will be added in Step 5), and vanilla extract.
On low speed, add about a third of the flour mixture and a third of the buttermilk, alternating until all of the flour and buttermilk is added to the batter. Add about 1 - 1 1/2 teaspoons (more if desired) of red food coloring gel to the mixture. Be sure not to over mix the batter — a few lumps are okay.
In a separate bowl, whip the egg whites together on high speed until they form foamy peaks, about 3-4 minutes.
Then, add the whipped egg whites to the batter and carefully fold them into the batter, scraping the bowl as needed until fully incorporated.
Next, evenly divide the batter in the 3 prepared pans. Bake for 22-27 minutes or until a toothpick comes out clean. Note, baking time may vary depending on your oven. Be sure not to overbake or your cake will be dry.
Once done, allow the cakes to cool in the pan on a wire rack until completely cooled.
Make the Frosting. In a large bowl, combine the softened cream cheese with the softened unsalted butter and beat on high until smooth and creamy. Next, mix in vanilla extract, salt, and gradually add the powdered sugar, mixing on low speed at first to prevent a sugar cloud. When the sugar is pretty much incorporated, whisk the frosting for about 2 minutes on high.
Assemble Cake. Slice off the domed tops of each cake layer (if they are any) to create a flat surface. Place the trimmed tops into a food processor and pulse into fine crumbs (you can also crumble them by hand, though the processor will give a finer texture). Then, place the first layer of cake on a serving plate or cake stand, and evenly spread the top of the cake layer with frosting. Next, add the second and third layers and repeat. Once the last layer is on top, frost the top and sides of the cake. Next, gently press red velvet crumbs along the bottom half of the cake along the sides for decoration. Finish by piping swirls of frosting on top using a star tip.
Refrigerate the cake for at least 20-30 minutes before slicing. Then, enjoy!