Heat the oven to 190 C / 375 F. Line a 12-cup muffin tin with paper liners or grease it well.
Grate the zucchini on the large holes of a box grater. Wrap it in a clean kitchen towel and squeeze hard until you've pressed out 2 to 3 tbsp of liquid.
Whisk the gluten-free flour, baking powder, baking soda, salt, garlic powder, and pepper together in a mixing bowl.
In a second bowl, whisk the eggs, milk, and olive oil until smooth.
Pour the wet ingredients into the dry and fold just until no dry streaks remain.
Fold in the squeezed zucchini, 1 cup (115 g) of the cheddar, and the green onion. Stop mixing as soon as it's combined, the batter goes dense if you overwork it.
Divide the batter evenly between the 12 muffin cups, filling each about three-quarters full. Top each with the remaining cheddar.
Bake for 20 to 24 minutes, until the tops are golden, a toothpick comes out clean, and the internal temp hits 200 F / 93 C.
Cool the muffins in the tin for 5 minutes, then transfer to a wire rack to finish cooling.