Peel and wash the carrots and cut them into diagonal slices. Cook in boiling salted water for about 7 minutes, then drain. Clean, wash and cut leek into rings. Place the vegetables alternately in a flat, damp-proof dish. Mix 150 g crème fraîche, milk and egg. Season with salt, pepper and nutmeg. Spread over the vegetables.
Grate cheese over them. Cook in the preheated oven (electric cooker: 200 °C/ gas: level 3) for about 40 minutes. In the meantime, wash and chop the herbs for the sauce. Warm up the rest of the crème fraîche and stir in the herbs. Season to taste with salt, pepper and lemon juice. Serve gratin and sauce with ham