Clean and wash the Brussels sprouts and cook in boiling salted water for about 15 minutes. Drain, catch the vegetable water and measure 1/8 litre. Cut ham into cubes. Heat butter in a saucepan, dust with flour and sauté. Deglaze with vegetable water, stock and milk while stirring and bring to the boil. Season with salt, pepper and nutmeg.
Grate cheese finely and add it to the sauce up to 100 g and let it melt in it. Season to taste again. Fill sprouts and ham into a greased casserole dish and spread the sauce over it. Sprinkle with remaining cheese and bake in a preheated oven (electric: 200 °C/ gas: level 3) for about 40 minutes. Serve garnished with parsley as desired