Rinse quinoa under cold running water. Cook in a pot of boiling salted water for 15 minutes. Drain and set aside.
Wash and finely chop the leeks. Peel and grate carrots. Wash, pat dry, and chop the parsley thinly.
In a skillet, heat 1 tablespoon of oil. Stir fry the leeks and carrots for 15 minutes. Season with salt and pepper.
Combine quinoa, carrots, leeks, eggs and parsley.
Form small patties.
Heat the remaining oil in a nonstick pan and cook the patties for 3 minutes on each side.
Drain on paper towels and transfer onto a serving dish.
Serve hot, warm or cold with a green salad.