Preheat your oven to 350 degrees. Grease 3 (9-inch) round cake pans, then place a round piece of parchment paper at the bottom of each and grease the parchment. Set these aside.
In a large mixing bowl, combine the flour, baking soda, salt, and sifted cocoa powder. Whisk this mixture for about 20 seconds, and then set it aside.
Using an electric stand mixer with the paddle attachment, beat together the sugar and butter until the mixture turns pale and fluffy. This will take a few minutes at high speed. Add the vegetable oil and make sure to scrape down the sides of the bowl.
Gradually blend in the eggs, one at a time, ensuring each addition is just combined before adding the next. Mix in the egg yolks and red food coloring, then scrape down the bowl.
In a liquid measuring cup, combine the buttermilk, vanilla extract, and vinegar. Working in three separate additions, start and finish with the flour mixture. Add 1/3 of the flour mixture, alternating with 1/2 of the buttermilk mixture. Mix each addition until just combined.
Scrape down the sides and bottom of the bowl, then gently fold the batter to ensure everything is evenly mixed.
Divide the batter equally among the three prepared baking pans, spreading it into an even layer. Bake these in the preheated oven for 30 minutes or until a toothpick inserted into the center of the cake comes out clean.
Allow the cake to cool in the pans for 10 minutes, then run a knife around the edges to loosen them. Invert the cake onto wire racks to cool completely.
Once the cake is cooled, frost them with Cream Cheese Frosting. Store the cake in an airtight container in the refrigerator.