Preheat the oven to 350°F.
Grease a 9 x 5-inch loaf pan and line it with parchment paper, leaving enough parchment hanging over the sides to easily lift the bread from the pan after baking.
In a medium bowl, whisk together the flour, baking soda, baking powder, kosher salt, cinnamon and nutmeg. Set aside.
In a large mixing bowl, whisk together the eggs, oil, brown sugar, granulated sugar and vanilla until smooth and well combined.
Fold the freshly shredded zucchini into the wet ingredients.
Don’t squeeze the zucchini dry. The natural moisture in the zucchini helps create an incredibly soft and moist loaf.
Add the dry ingredients to the wet ingredients and gently fold everything together just until you can no longer see streaks of flour.
Be careful not to overmix. Overmixing quick breads can make them dense instead of soft and tender.
Pour the batter into the prepared loaf pan and smooth the top.
Bake for 55–65 minutes, or until the center is set and a toothpick inserted into the middle comes out clean or with just a few moist crumbs.
If the top begins to brown too much before the center is finished baking, loosely cover the loaf with foil for the remainder of the baking time.
Allow the bread to cool in the pan for about 15 minutes before lifting it out and transferring it to a cooling rack.
Let the zucchini bread cool completely before adding the frosting.