Preheat oven to 400°F (200°C).
Grease muffin tin thoroughly with oil.
Grate zucchini and potatoes finely.
Place grated vegetables on clean towel.
Squeeze out excess moisture completely.
Transfer vegetables to large bowl.
Add beaten egg to mixture.
Mix in flour and cheese.
Add oil, salt, and pepper.
Stir in garlic powder and chives.
Divide mixture evenly among cups.
Press down firmly in cups.
Bake for 25-30 minutes until golden.
Cool for 5 minutes before removing.