Preheat your oven to 350°F (175°C).
Grate the zucchini and squeeze out excess moisture.
In a large mixing bowl, combine the grated zucchini with the gluten-free flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
In another bowl, whisk together the granulated sugar, brown sugar, eggs, vegetable oil, and vanilla extract until smooth.
Gradually add the dry ingredients to the wet ingredients and stir gently until just combined.
Divide the batter evenly among the muffin cups, filling each about two-thirds full.
Bake for 20-25 minutes, or until a toothpick inserted into the center comes out clean.
Allow the muffins to cool in the pan for about 5 minutes before transferring them to a wire rack.