Preheat the oven to 350°F (175°C).
Line a standard 12-cup muffin pan with paper liners.
Wash and grate the zucchini using the large holes of a box grater.
Place the shredded zucchini in a clean kitchen towel and gently squeeze to remove obvious excess moisture without drying it completely.
In a medium bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, and salt.
In a large bowl, whisk together the eggs, brown sugar, granulated sugar, vegetable oil, and vanilla extract until smooth.
Stir the shredded zucchini into the wet mixture.
Add the dry ingredients and gently fold just until combined.
Combine the granulated sugar and cinnamon for the topping in a small bowl.
Divide the batter evenly between the 12 prepared muffin cups, filling each approximately three-quarters full.
Sprinkle each muffin lightly with cinnamon sugar.
Bake for 18–22 minutes, until the tops spring back lightly and a toothpick inserted into the center comes out clean or with a few moist crumbs.
Cool in the muffin pan for 5 minutes.
Transfer the muffins to a wire rack and allow them to cool before serving.