Preheat the oven to 350 degrees. Combine the flour, baking powder, baking soda, cinnamon, and nutmeg in a medium bowl. Mix together the eggs, applesauce, and oil in a large bowl and beat well. Add the honey, bananas, and vanilla. Add the flour mixture slowly to the banana mixture. Mix well, but do not overbeat. Pour the mixture into a nonstick loaf pan. Bake until a toothpick inserted in the center comes out clean, about 35 to 45 minutes. Let the banana bread cool for 10 minutes in the pan. Remove the bread from the pan and let it cool completely, then slice into 1-inch thick slices. Let the banana bread dry out overnight. The next day, beat together the egg substitute, milk, and cinnamon. Place the banana bread slices into a casserole dish. Pour the egg mixture over the banana bread slices and place in the refrigerator for several hours. Dot the banana bread with the butter. Bake the banana bread slices until golden brown, about 15 to 17 minutes. | 
