Preheat oven to 180 degrees C. Spray a 20x30cm baking dish with non-stick cooking spray.
Heat butter in a frypan over medium heat. Stir in mushrooms, onion and pepper. Cook until soft and tender. Sprinkle flour over vegetables and stir to coat. Stir in milk and chicken stock. Cook until sauce thickens. Stir in broccoli, Parmesan, salt, pepper and nutmeg. Cook until Parmesan is melted.
Layer baking dish with 1/4 sauce, 1/4 pasta, 1/4 ham, 1/4 chicken and 1/4 Swiss. Repeat layers 3 times. Cover with foil.