In a large Dutch oven or heavy-bottomed pot, melt the butter over medium heat. Add onions and sugar and cook until soft and translucent, stirring occasionally, about 25 minutes. Add garlic, salt, and pepper. Continue cooking for about 90 minutes, stirring periodically and scraping the bottom of the pan with a wooden spatula to avoid burning. Reduce heat to medium-low as needed. The caramelized onions are done when they're very thick and amber/brown, almost paste-like.

Sprinkle flour over the browned onions, stirring constantly for 1 minute. Gently drizzle in the wine, scraping the bottom of the pot with a wooden spatula to loosen the browned bits. Add stock, Worcestershire, bay leaf, and thyme. Bring to a boil then reduce heat to maintain a simmer for 45 minutes. Remove from heat.

Remove bay leaf and thyme sprigs from pot. Add Balsamic vinegar. Taste and adjust seasonings as desired.

Preheat oven to 400 degrees F.

Arrange bread slices on baking sheet and bake 6-8 minutes until golden. Remove from oven and rub with garlic cloves.

Divide soup into ovenproof bowls and arrange on a rimmed baking sheet. Top each bowl with 2-3 slices of toast. Cover top of toast and soup with desired amount of cheese, about 1/2 cup per bowl. 

Set oven to broil setting. Place tray of soup bowl under broiler from about 3-5 minutes until cheese is melted and bubbling.

Serve immediately.