Combine flour, cinnamon, baking soda, and salt in a large bowl. Set aside. Peel and shred zucchini to get 2 cups. Remove any seeds before shredding.
Peel, core, and shred the Granny Smith apples to get 1 heaping cup. A little extra doesn't hurt. It's ok if the shredded apple darkens while making the recipe.
In a large mixing bowl, beat eggs for 1 minute. Add oil, applesauce, sugar, brown sugar, and vanilla. Mix for another minute. Fold in shredded apples and zucchini.
Pour this wet mixture into the large bowl with the dry ingredients. Stir by hand just until the ingredients are blended well. Do not over stir.
Use cooking spray to lightly coat three 8x4 bread loaf pans. Divide the batter between the three bread loaf pans. The pans should be about 3/4 full.
Bake for 55 minutes. This can vary by oven and altitude. To test for doneness, insert a toothpick in the center of a loaf. If it comes out clean, the bread is cooked through.
Allow loaves to cool 10 minutes before removing from pans. Finish cooling on a wire rack.
Notes
7 small bread loaf pans (6x2 inch) can also be used for this recipe. Fill each pan about 3/4 full and bake for 40 minutes at 350 degrees.