Peel the carrots and grate finely. Wash and clean the zucchini and also finely grate. Salt and leave to soak in water for about 10 minutes. Then squeeze well.
Peel the potatoes and grate finely. Wrap in a damp kitchen towel and squeeze. Let the vegetable juice stand for a bit, then drain it, leaving the settled starch on the bottom of the bowl.
Mix the zucchini, carrots and potatoes well with the egg and flour. Season with salt, pepper and nutmeg.
Then place heaps of the mixture in a pan (preferably coated) in hot oil and fry for 3-4 minutes until golden brown. Then turn them over and fry for another 3-4 minutes until golden brown. Fry all the carrot pancakes in batches like this until golden brown. Drain on paper towels. If desired, keep warm in the oven (approx. 70 °C) until all pancakes are done.
For the dip, peel the garlic and squeeze a bowl. Mix with the yogurt, tahini and lemon juice until smooth. Season to taste with salt and pepper.
Arrange the pancakes on plates, drizzle with the dip and garnish with parsley. Serve with lemon wedges.