Preheat the oven to 350°F (175°C) and grease a 9×5-inch loaf pan or line it with parchment paper.
Grate the zucchini and squeeze out excess moisture so it’s damp but not dripping.
Whisk together the flour, baking soda, baking powder, salt, and cinnamon in a bowl.
In a separate bowl, whisk the mashed bananas, melted oil, sugar, egg, and vanilla until smooth.
Stir the shredded zucchini into the wet mixture.
Add the dry ingredients to the wet and mix gently until just combined—do not overmix.
Fold in the chocolate chips and nuts if using.
Pour the batter into the loaf pan and smooth the top.
Bake for 50–60 minutes, or until a toothpick inserted into the center comes out clean.
Cool in the pan for 10 minutes, then transfer to a wire rack to finish cooling.