Preheat oven to 350°F (175°C) and grease/line a 9x5-inch loaf pan.
Grate zucchini and lightly squeeze excess moisture (don’t dry it out completely).
Whisk flour, sugars, cinnamon, baking soda, baking powder, and salt in a large bowl.
Whisk eggs, oil, applesauce (if using), and vanilla in another bowl until smooth.
Pour wet into dry and stir just until combined (don’t overmix).
Fold in zucchini and optional nuts or chocolate chips gently.
Pour batter into pan and bake 50–60 minutes until a toothpick comes out clean.
Cool 10 minutes in pan, then move to a rack and cool before slicing.