Preheat the oven to 350°F (175°C). Grease a 9×5-inch loaf pan or line it with parchment paper.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, ground cinnamon, ground nutmeg, and salt. Set aside.
In a large bowl, combine the granulated sugar, brown sugar, and vegetable oil. Beat in the eggs one at a time until well incorporated.
Add the mashed banana and grated zucchini to the wet ingredients and mix until combined.
Gradually add the dry ingredients to the wet ingredients, stirring just until combined. Do not overmix.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake for 55 to 60 minutes, or until a toothpick inserted into the center comes out clean.
Remove the bread from the oven and allow it to cool in the pan for 10 minutes.
Transfer the bread to a wire rack to cool completely before slicing.