Prepare the pans: Grease two 8 x 4-inch loaf pans or six mini loaf pans. Preheat the oven to 325°F (163°C).
Prep the fruits: Grate the zucchini using a box grater and set aside. Peel and dice the apple into small pieces.
Mix dry ingredients: In a large mixing bowl, whisk together the flour, cinnamon, salt, baking powder, and baking soda.
Mix wet ingredients: In a separate bowl, beat the eggs, vegetable oil (or applesauce), vanilla extract, white sugar, and brown sugar until well blended.
Combine wet and dry ingredients: Pour the wet ingredients into the dry ingredients and stir until just combined.
Add zucchini, apples, and nuts: Gently fold in the grated zucchini, diced apple, and chopped walnuts. Let the batter sit for 5 minutes.
Pour into pans: Divide the batter evenly between the prepared loaf pans.