Preheat the oven to 350°F (175°C). Grease a 9×5-inch loaf pan and set aside.
In a large mixing bowl, whisk together the sourdough starter, granulated sugar, brown sugar, vegetable oil, eggs, and vanilla extract until smooth and well combined.
In a separate bowl, sift together the all-purpose flour, baking soda, baking powder, salt, ground cinnamon, and ground nutmeg.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined. Do not overmix.
Fold in the grated zucchini and chopped walnuts (if using) until evenly distributed.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake in the preheated oven for 55 to 60 minutes, or until a toothpick inserted into the center comes out clean.
Remove the bread from the oven and let it cool in the pan for 10 minutes.
Transfer the bread to a wire rack and let it cool completely before slicing.