Coat 3 (9-inch) round cakepans with cooking spray; sprinkle 2 teaspoons flour evenly into pans, shaking to coat.
Combine remaining 3 cups flour and next 4 ingredients in a large bowl. Stir together eggs, applesauce, and oil; add to flour mixture, stirring just until dry ingredients are moistened. (Do not beat.) Stir in mashed banana, vanilla extract, and pineapple. Pour batter evenly into prepared pans.
Bake at 350° for 23 to 25 minutes or until a wooden pick inserted in center comes out clean. Cool layers in pans on wire racks 10 minutes. Remove layers from pans; cool completely on wire racks.
Spread Cream Cheese Frosting between layers and on top and sides of cake.
Orginia Hummingbird cake per slice: Calories 476 (45% from fat); Fat 24g (sat. 7.6); Chol 57mg; Sodium 191mg.