Peel and cut onions in half, then cut into slices.
In a 12 inch sauté pan, place butter, olive oil, onions and brown sugar.
Cook over medium low heat, stirring every 15 minutes, until the onions are a deep golden brown. This will take anywhere from 30-45 minutes. Cooking low and slow is the name of the game here.
Pour the beef broth into the 3 quart sauce pan. Add the balsamic glaze. Cook over medium heat until almost boiling.
Add the caramelized onions to the broth. Turn heat down to low and simmer soup for 5 minutes.
Set oven to broil and heat up.
While the broiler heats up, shred the cheese.
Place oven safe bowls on a baking sheet. Put 4 to 5 croutons in the bottom of each bowl. Ladle soup in each bowl filling a half inch from the top. Cover soup with shredded gruyere cheese.
Put baking sheet with soups under the broiler and broil until the soup is completely melted and the edges of the cheese are starting to toast. Keep a watchful eye and do not let the cheese burn.
Place hot bowl on dinner plate and serve immediately.