Grease two 8 x 4-inch pans or 6 mini loaf pans.
Preheat oven to 325 degrees F.
Assemble your ingredients. Mix flour, salt, baking powder, baking soda, nutmeg, and cinnamon together in a bowl.
Beat eggs, applesauce, vanilla, and sugar together in a large bowl.
Add dry ingredients to the creamed mixture and beat well.
Grate or zest the zucchini into small slivers. Stir into the mixture along with the walnuts until well combined.
Pour batter into prepared pans.
Bake for 45 to 60 minutes, or until tester inserted in the center comes out clean. My mini-loaf pans take about 40-50 minutes. Large-sized loaves take about 55-60 minutes.
Cool in pan on a rack for 20 minutes.
Remove bread from pan, and completely cool.