Preheat your oven to 350°F (175°C).
Squeeze out excess moisture from the grated zucchini and set aside.
In a large mixing bowl, combine the gluten-free flour, baking soda, baking powder, ground cinnamon, and salt. Stir until well mixed.
In another bowl, whisk together the granulated sugar, brown sugar, vegetable oil, eggs, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and gently stir until just combined. Fold in nuts or chocolate chips if using.
Divide the batter evenly among the muffin cups, filling each about ¾ full.
Bake for 20-25 minutes, or until a toothpick inserted into the center comes out clean. Allow to cool in the pan for 5 minutes before transferring to a wire rack.