Mix milk with two eggs, sour cream and the cheese. Season with salt, pepper and nutmeg.
Cut the mushrooms into thin pieces and fry them in a pan with a little oil, sprinkle with salt, pepper and the chopped parsley.
Peel the potatoes and cut them into thin slices. Grease an ovenproof dish with a little butter, place half of the potatoes in the dish slightly overlapping, spread the mushrooms on top and cover with the remaining potatoes.
Pour the milk mixture over them and bake at 160 °C for about 45 minutes.
Remove from the oven, let rest for 5 minutes, portion into pieces and sprinkle with some freshly ground pepper.