Clean the cauliflower and cut into florets. Peel and wash the potatoes and cut them into pieces. Pre-cook potatoes in boiling salted water for 10-15 minutes. Add the cauliflower florets about 5 minutes before the end and cook them.
Drain the potatoes and cauliflower in a sieve and leave to drain.
In the meantime peel onions and cut them into fine pieces. Melt the fat in a pot. Stir in flour, sweat briefly. Add milk and broth bit by bit while stirring. Bring to the boil, simmer for about 5 minutes, remove from heat.
Stir the mustard into the sauce. Season to taste with salt, pepper and nutmeg.
Wash the meat, dab dry and cut into small pieces. Heat oil in a pan. Fry the meat for 3-4 minutes, turning it over, and take it out. Spread the potatoes, cauliflower and meat in a greased, ovenproof casserole dish (22 cm Ø; 4.5 cm high).
Pour béchamel sauce over it. Bake in the preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: see manufacturer) for 20-25 minutes.
Wash parsley, shake dry, pluck off leaves and chop. Remove the casserole from the oven and sprinkle with parsley.