Sift first 7 ingredients into large bowl of electric mixer (or other bowl if mixer is not available). Add shortening and soup and beat at low to medium speed 2 minutes (or 300 strokes with spoon), scraping sides and bottom of bowl constantly. Add eggs and water and beat 2 minutes longer, scraping bowl frequently. Pour into two 9-inch layer pans lined on bottom with waxed paper. Bake in preheated moderate oven (350 degrees F.) 25 minutes or until done. Let stand in pans on cake racks 10 minutes, then turn out, peel off paper and turn cakes right side up; cool. Spread frosting between layers and on top of cake.
Frosting: Blend softened cream cheese with milk. Gradually beat in confectioners' sugar. Add vanilla. Mix until mixture is of frosting consistency.