Melt butter in large pot over medium heat. Add onions and cook until golden brown and caramelized, stirring regularly for about 30 minutes.
Mix in garlic and stir in vermouth.
Add beef broth, onion broth and thyme leaves, bringing to boil over high heat. Return to simmer and cook for 20 minutes, stirring occasionally.
Stir in vinegar, salt and pepper.
Pre-heat oven to broil.
Ladle soup servings into deep mugs or soup bowls. Place slices of baguette on top and then cheese.
Place soup servings on baking pan in broiler for 2-3 minutes – just enough time to melt the cheese.
Serve topped with sprigs of fresh thyme.