Preheat oven to 350ºF.
In a medium bowl, whisk together the flour, baking soda, salt, cinnamon, and nutmeg; set aside.
Shred zucchini; set aside.
Melt butter and allow to cool. In a large bowl, use a mixer to beat eggs and sugar until creamy. Add vanilla, 1/2 teaspoon lemon zest, applesauce, and butter. Mix well, then stir in 3 cups of the shredded zucchini.
Slowly add the dry ingredients to the wet, mixing just until smooth and moist.
Spray the muffin tin with cooking spray.
Divide the batter evenly between the muffin cups; bake for 20-22 minutes or until a toothpick inserted into the center of a muffin comes out clean.
Cool slightly, then transfer to a cooling rack. Allow to cool completely before serving.