In a large saucepan, sauté onions in olive oil on medium heat until browned, but not burned (40 minutes) Add sugar about 10 minutes into the process to help the onions carmelize.
Add garlic and sauté with the onions for 2 minutes. Add the stock, vermouth or wine, bay leaf, and thyme. Cover partially and simmer until the flavors are well for about 30 minutes. Season to taste with salt and pepper and remove the bay leaf.
Serve in oven-safe soup bowls. Ladle the soup into the bowls, cover with croutons and sprinkle with cheese. Put into the broiler for 10 minutes at 350 degrees F, or until the cheese bubbles and is slightly browned.