Make the batter: Preheat oven to 350 degrees F. Using a small brush, lightly coat two 9-inch cake pans with butter or vegetable-oil cooking spray. Dust the pans with flour, tap out any excess, and set aside. In a large bowl, using a mixer set on medium-high speed, beat the butter and sugar until light. Add the yolks and continue to beat for 1 more minute. In a small bowl, stir the food coloring, the vanilla, and the cocoa together. Reduce mixer speed to low and add the cocoa paste to the batter. In a glass measure, mix the salt with the buttermilk and add it to the batter by thirds, alternating with the flour. In another small bowl, mix the baking soda with the vinegar and blend into the batter.
Bake the cake: Divide the batter equally between the pans and spread evenly. Bake on the middle rack of the oven until a tester inserted in the center of each layer comes out clean — about 30 minutes. Cool in the cake pans on a wire rack for 15 minutes. Using a knife, loosen cake layers from the sides of the pans and invert the layers onto wire rack to cool completely.
Ice the cake: Use a serrated knife to split each layer into 2 even layers. Line the edges of a cake plate with 3-inch-wide strips of waxed or parchment paper and place a cake layer, trimmed side down, on top. Evenly spread 1 cup of icing over the layer and repeat with 2 other layers. Top with the final layer and cover the top and sides with remaining icing.