Preheat oven to 350°F (175°C). Grease and flour a 9x5 inch loaf pan. Finely shred the zucchini, then place it in a clean kitchen towel and squeeze firmly to remove as much excess water as possible. Set aside.

In a large bowl, mash the bananas. Whisk in the granulated sugar, brown sugar, oil, eggs, and vanilla extract until well combined.

In a separate medium bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, and nutmeg.

Add the dry ingredients to the wet ingredients and mix with a spatula until just combined. Do not overmix. Gently fold in the squeezed, shredded zucchini.

Pour the batter into the prepared loaf pan and spread evenly. Bake for 55-65 minutes, or until a toothpick inserted into the center comes out clean. If the top is browning too quickly, tent loosely with foil for the last 15 minutes.

Let the bread cool in the pan on a wire rack for 15 minutes before inverting it out of the pan to cool completely. Slice and serve.