Preheat the oven to 350F. Prepare the desired cake tins: use this recipe for 2 or 3, 8-inch rounds; 2, 10-inch rounds; 13x17-inch jelly roll pan for a sheet cake; also makes 24 cupcakes. Line pans with parchment paper and line cupcake tin with cups.
In a large mixing bowl, beat together the softened butter, sugar and vanilla for a few minutes, until fluffy. Add the egg whites or eggs and beat again until creamy and smooth. Using only egg whites yields a more 'white' cake; using whole eggs will give the cake a soft yellow color. Next, pour in the milk (I recommend using warm milk).
NOTE: the batter may look curdled once you add the milk! It is not. This happens because the milk causes the butter particles to clump together. Just continue with the recipe.
In a separate bowl, combine all the dry ingredients: flour, baking powder and salt. Sift the dry ingredients into the cake batter and whisk by hand to avoid over-mixing the batter.
Divide the cake batter evenly between prepared pans. Bake in preheated oven for approximately 30 minutes for 3, 8-inch rounds; or until a toothpick inserted into the center comes out clean.
Allow the cakes to cool in the pans for about 10 minutes, then invert onto cooling rack to cool completely. Frost and fill cake once the cake is completely cooled. IF not using the layers right away, wrap with plastic wrap to avoid drying.