Cream butter; gradually add sugar, beating well.
Combine flour, baking powder, and salt; add to creamed mixture alternately with milk, beginning and ending with flour mixture. Stir in vanilla.
Beat egg whites (at room temperature) until stiff peaks form; fold into batter.
Spoon batter into 2 waxed paper-lined and greased 9-inch round cake pans. Bake at 350° for 35 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes; remove from pans, and cool completely.
Spread filling between layers of cake, and chill. Spread top and sides of cake with frosting.