For the béchamel sauce, heat the fat in a pot, stir in the flour and sauté. Deglaze with milk. Add bay leaf and simmer for about 10 minutes at low heat while stirring.
Season with salt and cayenne pepper. In the meantime, cook the tortellini in plenty of boiling salted water for about 10 minutes and drain. Clean and slice the mushrooms. Peel and finely dice onion.
Heat the oil in a pan. Brown the mushrooms and onion in it. Season with salt and pepper, remove and set aside. Cut ham into fine cubes. Layer tortellini with béchamel, mushroom-onion mixture, peas and diced ham in an ovenproof dish (30 x 20 cm; approx. 2.5 l capacity).
Coarsely grate the cheese and spread it on the casserole. Bake in the preheated oven (electric cooker: 175 °C/ gas: level 2) for approx. 1 hour. Serve sprinkled with parsley cut into strips.