Preheat the oven to 325 degrees, and set the rack to the middle position. Grease two 8 x 4-inch loaf pans with nonstick cooking spray.
In a medium bowl, combine the flour, cinnamon, nutmeg, baking soda, baking powder and salt. Mix well using a whisk.
In a large bowl, whisk the eggs with the sugar. Add the grated zucchini, melted butter, and vanilla extract; Stir to combine using a wooden spoon or rubber spatula.
Add the dry ingredients to the liquid ingredients, and mix until just combined. Add the nuts, then divide the batter evenly into the prepared pans. Bake for 60 to 65 minutes, or until a cake tester comes out clean. Set the pans on a wire rack and let cool for about 10 minutes, then turn the loaves out on the rack to cool down completely.