Preheat the oven to 350°F (175°C). Grease a 9×5-inch loaf pan and set aside.
In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, salt, ground cinnamon, and ground nutmeg.
In a large bowl, beat the granulated sugar, brown sugar, and eggs until well combined.
Add the vegetable oil and vanilla extract to the sugar and egg mixture, and mix until smooth.
Fold in the grated zucchini and mashed bananas until evenly distributed.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined. Do not overmix.
If using, fold in the chopped walnuts.
Pour the batter into the prepared loaf pan and spread it evenly.
Bake for 55 to 65 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.