For the sauce:
1. In a frying pan heat the oil and sauté the onion 5-6 minutes. Add the mushrooms, reduce the heat and cook for 10 minutes. Season to taste.
2. Cut the eggs lengthwise, remove the yolk and sieve over the pan. Mix well with mushrooms and onions. Stuff the eggs with the mixture.
3. Prepare the sauce. In a frying pan melt the butter, add the flour and cook for 2 minutes. Pour the hot milk stirring constantly and boil 2-3 minutes. Correct seasonings and add cream. Cook for 2-3 minutes more, without boiling. Add half of the cheese.
4. Place the eggs in an oven dish, cover with the sauce and sprinkle with remaining cheese. Broil until hot and nicely brown.