In a heavy kettle, brown meat in butter. Season lightly with salt and pepper. Add chopped onion and saute until clear. Mix in tomato paste, vinegar, garlic and half of the water. Add bay leaf. Cover and simmer 1 hour, adding additional water as needed. Add white onions and mushrooms. Cover and simmer 1 more hour or until meat and onions are tender. Add cheese, cover and cook 5 minutes, or until cheese melts.