Preheat oven to 325 degrees F and grease two 9x5-inch or 8x4-inch bread pans with non-stick spray.
In a stand mixer or large bowl with a hand mixer, beat together the eggs, vegetable oil, sugar, and vanilla until combined.
In a separate large bowl, whisk together the flour, salt, cinnamon, baking powder, and baking soda.
Add the dry ingredients to the wet ingredients in 2 separate additions, mixing between each one. Then beat for 1 more minute making sure to push the sides down so everything is well combined. The mixture will appear dry and thick, this is normal.
Add in the grated zucchini and 1 cup of walnuts and beat for 1 minute, scraping down the sides as needed.
Divide the batter between the two loaf pans and top each loaf with 1/2 cup of chopped walnuts and 2 tablespoons of light brown sugar.
Bake for 50 to 60 minutes until a toothpick or cake tester comes clean from the center of the leaves.
Remove from the oven and allow the bread to cool in the pans for 20 minutes, remove from pan and let cool completely.