Preheat your oven to 350°F (175°C). Grease a 9x5-inch loaf pan or line it with parchment paper.
Grate the zucchini and lightly squeeze to remove excess moisture. Mash the bananas until smooth. In a large mixing bowl, whisk together mashed bananas, zucchini, eggs, oil, brown sugar, and vanilla extract until smooth.
In a medium bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
Gradually fold the dry ingredients into the wet mixture. Mix until just combined—do not overmix.
Gently fold in nuts, chocolate chips, or other add-ins if desired.
Pour the batter into the prepared loaf pan. Bake for 55–60 minutes or until a toothpick inserted in the center comes out clean. Let the bread cool in the pan for 10 minutes, then transfer it to a wire rack to cool completely before slicing.