Preheat your oven to 350°F (175°C). Grease a 9x5-inch loaf pan or line it with parchment paper.
In a large bowl, combine the mashed bananas, grated zucchini, vegetable oil, granulated sugar, brown sugar, eggs, and vanilla extract. Mix well until fully combined.
In another bowl, whisk together the flour, baking soda, baking powder, salt, and ground cinnamon.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Be careful not to overmix.
If using, fold in the chopped nuts and chocolate chips.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean. If the top is browning too quickly, cover it loosely with aluminum foil.
Once baked, remove from the oven and let it cool in the pan for about 10 minutes. Then transfer the bread to a wire rack to cool completely.