Cream shortening; gradually add sugar, beating well. Add egg yolks, one at a time, beating well after each addition.
Combine flour, baking powder, and salt; add to creamed mixture alternately with milk, beginning and ending with flour mixture. Mix well after each addition. Stir in vanilla.
Beat egg whites (at room temperature) until stiff peaks form; fold into batter.
Divide batter in half. Add melted chocolate to one-half of batter; mix well.
Line three 9-inch round checkerboard cake pans with greased waxed paper; grease sides of pan. Place checkerboard divider rings into one prepared pan. Spoon one-third of chocolate batter into center and outer rings; spoon one-third of white batter into middle ring, filling half full (a pastry bag may be used to pipe batters into rings). Smooth batter with a small spatula. Carefully remove checkerboard rings. Rinse rings and dry thoroughly before placing in next pan. Repeat procedure with second pan.
Spoon white batter into the center and outer rings of third pan, filling half full; spoon chocolate batter into middle ring, filling half full.
Bake at 350° for 20 minutes or until a wooden pick inserted in center comes out clean. Cool the layers in pans 10 minutes; remove layers from pans, and let cool completely.
Spread Chocolate Butter Frosting between layers, placing the white outer layer in the center. Frost top and sides of cake with remaining frosting.