Set the oven to 350°F (175°C) and lightly grease a 9×5-inch loaf pan.
Mash bananas in a large bowl until smooth. Stir in eggs, sugar, and oil.
Grate the zucchini, press out the extra liquid with a towel, and mix it into the wet ingredients.
In another bowl, combine the flour, baking soda, baking powder, cinnamon, nutmeg, and salt with a whisk.
Combine wet and dry ingredients gently, avoiding overmixing. Stir in nuts or chocolate chips if using.
Transfer the batter into the loaf pan and bake for 50–60 minutes, or until a toothpick inserted in the center comes out clean.
Let the bread cool on a wire rack for 10–15 minutes before cutting into slices.
