Preheat oven to 350°F/180°C. Grease two 8-inch-by-4-inch (20-centimeter-by-10-centimeter) loaf pans with nonstick spray.
After shredding zucchini, line a bowl with a paper towel or a kitchen towel. Let zucchini set for a few minutes in towel, then squeeze out excess liquid.
Combine flour, baking soda, baking powder and spices in a large bowl. In a separate bowl, whisk oil, eggs, vanilla and sugars.
Add zucchini and nuts to flour mixture, then pour egg mixture over it. Gently stir to combine until flour is no longer visible. Divide batter between 2 loaf pans.
Bake 45 to 50 minutes, or until a toothpick inserted into the center comes out clean. Allow loaves to cool in pan 10 minutes, then turn them out onto a wire rack to cool completely.
Loaves will keep in an airtight container for several days. They can be wrapped in foil and frozen for up to 3 months. Thaw in the fridge overnight or in a warm oven for 20 minutes.