Preheat oven to 325°. Beat butter at medium speed with an electric stand mixer until creamy. Gradually add sugar, beating until light and fluffy. Add orange zest and vanilla; beat until blended. Combine flour and next 2 ingredients; add to butter mixture alternately with milk, beginning and ending with flour mixture. Beat at low speed just until blended after each addition.
Beat egg whites at high speed until stiff peaks form. Stir about one-third of egg whites into batter; fold in remaining egg whites in 2 batches. Spoon into 3 greased (with shortening) and floured 9-inch round cake pans.
Bake at 325° for 25 minutes or until a wooden pick inserted in center comes out clean. Cool in pans on wire racks 10 minutes; remove from pans to wire racks, and cool completely (about 1 hour). Frost as desired.
Note: Cake layers may be baked in 3 (8-inch) square disposable aluminum foil pans. Increase bake time to 26 to 30 minutes.