Cut the carrots into slices. Cook in boiling salted water for about 7 minutes, place on a sieve and drain. Cut leek into rings. Layer the vegetables in a flat, ovenproof dish. Whisk sour cream, milk and egg, season with salt, pepper and nutmeg. Spread over the gratin.
Sprinkle with cheese. Bake gratin in a preheated oven (electric cooker: 200 °C/ gas: level 3/ convection oven 175 °C) for approx. 40 minutes. Cut chives into small rolls. Chop dill and parsley. Carefully warm up the crème fraîche, stir in the herbs and season with salt, pepper and lemon juice. Serve gratin with sauce and ham