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 until well combined.
In a large bowl, beat the granulated sugar, brown sugar, and eggs together until smooth and creamy.
Add the vegetable oil and vanilla extract to the wet mixture and mix until fully incorporated.
Fold the shredded zucchini and mashed banana into the wet ingredients 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 evenly throughout the batter.
Pour the batter into the prepared loaf pan and spread it out evenly.
Bake in the preheated oven 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 and serving.