Place zucchini on several layers of paper towels, and cover with additional paper towel. Let stand 5 minutes, pressing down occasionally. Set aside.
Combine flour and next 5 ingredients (flour through baking powder) in a large bowl, and stir well; make a well in center of mixture. Combine zucchini, applesauce, egg substitute, oil, and vanilla; add to dry ingredients, stirring just until dry ingredients are moistened.
Divide batter evenly between 2 (7 1/2 x 3-inch) loaf pans coated with cooking spray. Bake at 350° for 1 hour and 15 minutes or until a wooden pick inserted in center comes out clean. Let cool in pans 10 minutes on a wire rack; remove from pans, and let cool completely on wire rack.