Preheat the oven to 325 F (165 degrees C). Grease two 8x4 inch loaf pans with butter or non-stick cooking spray and line them with parchment paper, letting it hang over the edge. Set aside.
In a medium bowl whisk together flour, salt, baking powder, baking soda, cinnamon, and nutmeg until combined.
In a large bowl using a handheld mixer or whisk beat the eggs, oil, vanilla, brown sugar, and granulated sugar until combined.
Slowly add the flour mixture into the egg mixture and beat well until combined.
Mix in the shredded zucchini and walnuts.
Pour the batter evenly into the prepared loaf pans and bake for 40-60 minutes, or until a toothpick inserted in the center comes out clean.
Cool in pans on a cooling rack for about 20 minutes, then remove from the pans and allow to cool completely.