In a large skillet, add the sliced onions, olive oil and white sugar and bring to sizzling saute over medium heat. Then reduce heat to low and caramelize for 30 minutes to 1 hour. Stir often as the onions soften and caramelize/turn brown.
In a large saucepan or soup pot, bring the beef broth, white wine, fresh or dried thyme to a rolling boil. When the onions are done caramelizing, slide them carefully into the broth and continue to simmer over low heat for another 10-15 minutes to allow onion flavors to seep into the soup.
Ladle the soup into oven-safe serving bowls and add a slice or two of bread and a slice or pinchful of shredded cheese over the top.
Broil (1 rack lower) for 1-2 minutes, or until golden brown but not burnt. Do NOT walk away from the oven while broiling. You don't want to forget they are in there! Remove from the oven and let cool slightly before serving.
Serve French Onion Soup with fresh veggies.