Preheat oven to 350°F. Spray a 9x5 inch loaf pan with nonstick spray.
Grate zucchini and wrap in cheesecloth or a clean towel. Squeeze to remove as much moisture as possible, repeating until all excess moisture has been removed. Set aside.
In a medium mixing bowl, combine the flour, cinnamon, baking powder, baking soda, salt, and nutmeg (optional). Mix well.
In a separate large mixing bowl, combine the mashed banana, oil, sugars, eggs, and vanilla extract. Stir in the grated zucchini.
Add the flour mixture to the banana zucchini mixture. Stir just until combined.
Pour into prepared loaf pan. Bake at 350°F for 70-75 minutes or until a toothpick inserted in the center comes out clean.
Cool on a wire rack for 10-15 minutes before removing from pan. Enjoy immediately or transfer to wire rack to cool completely.