Peel, wash and coarsely chop the potatoes. Cover and cook in salted water for about 20 minutes. Clean and wash the Brussels sprouts and stew them in boiling salted water for 10-15 minutes.
Onion and soup greens peel or clean, wash and cut into fine cubes. Heat the oil. Fry the minced meat for about 5 minutes. Add the diced vegetables and fry for another 5 minutes. Season with salt, pepper and 1 pinch of sugar.
Add tomato paste and sauté briefly. Stir in the tomatoes, bring to the boil and simmer everything for about 5 minutes.
Drain the potatoes. Add milk and butter and mash finely. Season to taste with salt and nutmeg.
Layer the purée, bolognese and Brussels sprouts in a greased casserole dish. Grate the cheese and sprinkle over it. Bake in a hot oven (electric cooker: 200 °C/circulating air: 175 °C/gas: see manufacturer) for about 20 minutes.