Wash Jerusalem artichokes thoroughly, cover with cold water and bring to the boil. Cover and cook for approx. 10 minutes (depending on the variety, it may take longer!). In the meantime, peel, wash and cut the carrots into pieces.
Clean the leek, wash it and cut it into rings. Cook carrots and leek in 500 ml boiling salted water for about 10 minutes. Drain the Jerusalem Artichoke, rinse and peel. Cut Jerusalem Artichoke in half or in pieces, depending on size.
Put the carrots and leeks on a sieve and collect the vegetable water. Measure out 300 ml of vegetable water. Mix the vegetables and put them into one large or four small, greased casserole dishes. Peel and finely chop the onion.
Heat the fat in a pot and fry the onion in it. Add flour and sauté briefly. Add 300 ml vegetable water and milk while stirring, bring to the boil and simmer for 4-5 minutes. Stir 40 g cheese into the sauce and melt in it.
Season the cheese sauce with salt and pepper and pour over the vegetables. Sprinkle with 40 g cheese and sunflower seeds and bake in a preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for approx. 30 minutes.