Preheat oven to 325°. Beat butter and sugar at medium speed with a heavy-duty electric stand mixer until fluffy. Gradually add egg whites, one-third at a time, beating well after each addition.
Sift together cake flour and baking powder; gradually add to butter mixture alternately with 1 cup water, beginning and ending with flour mixture. Stir in vanilla. Pour batter into a greased and floured 13- x 9-inch pan.
Bake at 325° for 45 to 50 minutes or until a wooden pick inserted in center comes out clean. Cool completely in pan on a wire rack (about 1 hour). Remove from pan to a serving platter. Spread top and sides of cake with frosting.