1. Heat butter and oil in medium skillet. Add onions and cook over low-medium heat for 30 minutes, until dark brown, stirring occasionally. Add parsley, remove from pan and set aside.
2. Butter bread. Place buttered side down on a large skillet or griddle. Add 3 extra thin slices of cheese on each side of bread. (6 slices on each sandwich total).
3. Place onions on one side of bread. When cheese has melted put sandwiches together and remove from pan. Cut in half and serve immediately with a side of hot beef broth if desired.