Start by finely grating the carrots and zucchini. Place the grated zucchini in a clean kitchen towel and squeeze out as much moisture as possible—this helps the nuggets stay crispy.
In a large mixing bowl, combine the grated vegetables with the beaten egg, toasted panko breadcrumbs, Parmesan, garlic powder, and thyme. Mix everything thoroughly until the mixture is sticky and holds together well.
Shape the mixture into small, oval or rectangular nuggets about 2 inches long, pressing firmly to ensure they hold their shape.
If baking, preheat your oven to 200°C (392°F). Place the nuggets on a lined baking sheet, brush or spray lightly with oil, and bake for 15-20 minutes, flipping halfway, until golden brown and crispy.
If frying, heat enough oil in a skillet or deep fryer to cover the nuggets about 1 inch deep, around 180°C (356°F). Carefully lower the nuggets into the hot oil and fry for about 3-4 minutes, turning occasionally, until they are golden and crispy. Use a slotted spoon to remove them and drain on paper towels.
For an air fryer, arrange the nuggets in a single layer in the basket, spray lightly with oil, and air fry at 200°C (392°F) for 10-12 minutes, shaking the basket halfway through for even crispness.
Once cooked, transfer the nuggets to a wire rack or paper towels to drain excess oil. Let them rest for a minute or two until they are crispy and fragrant.
Serve hot with your favorite dips or sauces for an irresistible, veggie-packed snack or main course.