Preheat oven to 375°F. Grease or line a 9×5 loaf pan with parchment.
Shred zucchini and apple. Lightly blot excess moisture, but do not squeeze dry.
In a large bowl, mix zucchini, apple, applesauce (or eggs), oil, vanilla, granulated sugar, and brown sugar.
In a separate bowl, whisk flour, salt, baking soda, and cinnamon.
Add dry ingredients to wet ingredients and stir until just combined.
Let the batter rest for 10–15 minutes for a softer, moist crumb.
Pour into the prepared loaf pan.
Bake 70–75 minutes, checking at 60 minutes. A toothpick should come out clean or with moist crumbs.
Cool completely before slicing.