Caramelize the Onions: Heat butter and olive oil in a large pot over medium heat. Add onions and cook slowly, stirring occasionally, for about 45 minutes until golden brown.
Add Garlic and Thyme: Stir in minced garlic and dried thyme; cook for 1 minute.
Simmer the Soup: Add beef broth, chicken broth, Worcestershire sauce, and bay leaf. Simmer for 20 minutes. Season with salt and pepper to taste.
Prepare the Bowls: Divide soup into oven-safe bowls. Top with crostinis or croutons and shredded cheese.
Broil the Soup: Broil the bowls for 2-3 minutes until cheese is melted and bubbly. Serve hot.