Wash the potatoes thoroughly, bring them to the boil in a saucepan of water, cover and cook for about 15 minutes. In the meantime clean broccoli and cauliflower, wash and cut florets from the stems.
Peel, wash and cut the carrots into pieces. Bring the stock to the boil in a pot. Add the cauliflower and carrots, bring to the boil again, cover and cook over medium heat for about 12 minutes. After 5 minutes of cooking time add the broccoli.
Peel and finely chop the onion. Pour the vegetables into a sieve and collect the stock. Measure out 400 ml stock. Drain potatoes, quench and peel. Heat the fat in a pot, fry the onion in it at low heat, dust with flour, sweat it and gradually add the stock and milk.
Bring to the boil while stirring, stir in 25 g of cheese and season to taste with salt, pepper and sugar. Fill potatoes and vegetables into an ovenproof dish, pour sauce over it and sprinkle with 25 g cheese. Bake in the preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for about 20 minutes.
Remove from the oven and serve garnished with chervil.