Thinly slice the onions. In a large pot, melt butter over medium heat. Add onions and cook slowly, stirring occasionally until caramelized, about 30 minutes.

Add sugar, thyme, and bay leaf to the onions. Continue cooking for another 10 minutes.

Pour in white wine to deglaze the pan, scraping up any browned bits from the bottom. Let it cook for 5 minutes.

Add the beef broth, bring to a simmer, and cook for 20 minutes to blend flavors.

Remove thyme sprigs and bay leaf. Preheat oven broiler.

Ladle the soup into ovenproof bowls, top with a slice of French bread and shredded cheese. Place bowls on a baking sheet.

Broil in the oven until cheese is bubbling and golden, about 3 minutes.