Place a large pot over medium heat. Add onions, butter, Worcestershire sauce, vinegar, garlic, brown sugar, salt, and pepper.
Cook for 30 minutes until the onions begin to brown and caramelize, stirring occasionally.
Stir in the flour and let cook for 2-3 more minutes.
Add the broth and thyme. Cook on low for 20 minutes (or let simmer for 40 minutes).
Place in individual bowls, and slice a small piece of bread and place on top of the soup. Cover with one slice of cheese and broil for 3 minutes or until browned and bubbly.