Preheat the oven to 350 degrees F. Grease two 8-inch cake pans. Line the bottoms with parchment paper and grease the paper.
Sift the flour, cocoa, and baking soda into a bowl and whisk briefly to combine; set aside. Stir the red food color into the buttermilk and set aside.
In a large mixing bowl, cream the butter with the brown sugar, vanilla, and salt on medium-low speed until light and fluffy, 3 to 5 minutes. Add the eggs and egg yolks slowly, beating and scraping the bowl to ensure that they are completely incorporated. On low speed, add the dry ingredients alternately with the colored buttermilk. To prevent streaking in the cake, be sure to scrape the sides of the bowl well as you mix the batter. Finally, stir in the vinegar by hand. Divide the batter between the cake pans.
Bake for 35 to 40 minutes, or until a toothpick or cake tester inserted in the center comes out clean. Let the layers cool in the pans for 10 minutes. Then turn them out onto a wire rack, peel off the paper, and let cool completely.
Make the frosting using 8 ounces cream cheese, 1 stick unsalted butter, 4 cups confectioners' sugar, and 2 teaspoons vanilla extract.
To decorate the cake, place one layer bottom side up on a cake plate. Spread 3/4 cup of the cream cheese frosting evenly over the cake right to the edges. Add the second layer and use the remaining frosting to decorate the sides and top by gently swirling it over the cake.
Place the cream cheese and butter in a mixing bowl and beat with an electric mixer on medium speed until completely blended. Sift the confectioners' sugar onto the mixture in several additions, beating thoroughly in between. Add the vanilla and beat until the frosting is light and fluffy but still holds its shape, 3 to 5 minutes. Use immediately.
Do not use reduced-fat or nonfat cream cheese. The consistency will not be the same.
Excerpted from Desserts From the Famous Loveless Cafe by Alisa Huntsman (Artisan Books). Copyright 2011. Photographs by Karen Mordechai.