Preheat the oven to 350°F.
Wash the zucchini well and trim off the stem. Using the large holes on a box grater, grate the zucchini until you have roughly 2 cups.
In a large mixing bowl, whisk together the eggs, granulated sugar, brown sugar, applesauce, oil, and vanilla extract until smooth and well combined.
Stir the grated zucchini into the wet mixture.
In a separate bowl, whisk together the flour, baking powder, baking soda, salt, and cinnamon.
Add the dry ingredients to the wet ingredients and stir until just combined. Avoid overmixing the batter.
Fold in the chopped walnuts gently.
Grease an 8.5 x 4.5-inch loaf pan with butter or nonstick spray.
Pour the batter evenly into the prepared loaf pan.
Bake the Zucchini Bread for about 60 minutes or until a toothpick inserted into the center comes out clean.
Let the loaf cool in the pan for 5 minutes before transferring it to a wire rack to cool completely.
Slice and serve once cooled.