Preheat the oven to 180°C (350°F) and grease a muffin tin.
Place the grated zucchini, carrot, and potato in a clean kitchen towel and squeeze out excess moisture.
In a large bowl, whisk together eggs, olive oil, salt, black pepper, baking powder, and garlic powder.
Stir in the flour, Parmesan cheese, and cheddar cheese until combined.
Fold in the grated vegetables and green onions (if using).
Spoon the mixture evenly into the prepared muffin tin.
Bake for 20-25 minutes or until golden brown and firm to the touch.
Let the muffins cool slightly before removing them from the tin. Serve warm and enjoy!