Preheat oven to 350 degrees F. Butter and flour the bottom and sides of a 9-by-5-inch loaf pan and set aside. Sift together the flours, cinnamon, nutmeg, baking soda, baking powder and salt in a large bowl.

In a separate large bowl (or bowl of a stand mixer), beat together the sugars, oil, eggs and vanilla. Add shredded zucchini and sweet potato and stir to combine. Add dry ingredients and stir until just combined. Fold in chopped walnuts, if desired.

Pour batter into prepared pan and bake until a toothpick inserted in the center of the loaf comes out clean, about 1 hour 20 minutes. Halfway through baking, cover pan loosely with foil if top of loaf is browning too quickly. Remove bread from oven and cool 15 minutes in loaf pan on a cooling rack. Using a spatula or butter knife, loosen the edges of the bread and remove from loaf pan. Place bread on cooling rack and cool completely before slicing or serving.

Store bread wrapped tightly in foil at room temperature for up to 3 days.