Grease and lightly flour two 8 x 1 1/2 inch or 9 x 1 1/2 inch round baking pans or grease one 13x9x2 inch baking pan; set the pan(s) aside. Stir together flour, baking powder, baking soda and salt; set aside.
In a large mixing bowl beat shortening with an electric mixer on medium to high speed for 30 seconds. Add sugar and vanilla; beat till well combined. Add egg whites, one at a time, beating well after each. Add dry mixture and buttermilk alternately to beaten mixture, beating on low speed after each addition just till combined. Pour batter into the prepared pan(s).
Bake in a 350 degree oven for 30 to 35 minutes or till a wooden toothpick comes out clean. Cool layer cakes in pans on wire racks for 10 minutes. Remove layer cakes from pans. Cool thoroughly on racks. Or, place 13x9 inch cake in pan on a wire rack; cool thoroughly. Frost with desired frosting.
Tip: You can use the equivalent of butter or margarine in place of the shortening, if desired. But for a whiter cake use shortening.