Clean the Brussels sprouts and cook in boiling salted water for 18-20 minutes. Peel and wash carrots and cut them diagonally into thin slices. Melt butter, add carrots and season with salt and some sugar. After 1-2 minutes add 100 ml water and simmer covered for about 4 minutes. Cut dumplings into slices. Whisk eggs and milk and season with salt, pepper and some nutmeg.
Heat oil in a large coated pan and fry the dumpling slices in 1-2 portions on both sides until golden brown. Drain the carrots. Drain the Brussels sprouts, quench and halve them. Put the carrots, Brussels sprouts, dumplings and cured pork in 4 portion bowls and pour on egg milk. Grate cheese and sprinkle over the casseroles. Bake the casseroles in a preheated oven (electric range: 200 °C/ convection oven: 175 °C/ gas: level 3) for 30-35 minutes