Peel, wash and chop the potatoes and carrots. Boil potatoes and carrots covered with salted water and cook for about 20 minutes. Clean, wash and dry mushrooms.
Peel and finely chop the onion. Heat the oil in a pan. Fry the mushrooms and onions for 3-4 minutes. Season with salt and pepper. Drain potatoes and carrots, collect vegetable water and measure 1/8 litre.
Coarsely mash the potatoes and carrots. Stir in vegetable water and 1/8 litre milk. Season to taste with salt, pepper and nutmeg. Grease a casserole dish. Put mashed potatoes into the dish.
Spread mushrooms on it. Mix the egg and 5 tablespoons of milk. Season with salt and pepper and pour over the mushrooms. Sprinkle with cheese. Bake in the preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for about 10 minutes.
Serve mushroom casserole garnished with parsley. Black Forest ham tastes good with it.