Thoroughly butter two 8- or 9-inch round cake pans.
Carefully separate the eggs, making sure not to get any yolk in the whites. Put the whites aside at room temperature to be beaten later.
Cream the butter and sugar together. Beat in the egg yolks, add the vanilla, and set aside. Sift together the cake flour, baking powder, baking soda, and salt.
Beat the egg whites until they are fluffy, but not at all dry.
Mix the dry ingredients and buttermilk alternately into the egg and butter mixture. Do not overbeat. Then gently fold in the egg whites.
Fill your pans about two-thirds full. Bake in the preheated oven for 35 to 40 minutes.