1. In a large skillet, melt the butter over medium heat. Add the thinly sliced onions and cook, stirring occasionally, until they are golden brown and caramelized, about 20-25 minutes.

2. Once the onions are caramelized, add the ground beef and minced garlic to the skillet. Cook, breaking up the meat with a spatula, until the beef is browned and cooked through. Drain any excess fat if necessary.

3. Stir in the beef broth, Worcestershire sauce, ketchup, Dijon mustard, soy sauce, salt, and pepper. Allow the mixture to simmer for 10-15 minutes, stirring occasionally, until the sauce has thickened to a sloppy joe-like consistency.

4. While the beef mixture is simmering, lightly toast the hamburger buns under a broiler or in a toaster oven.

5. Spoon the French Onion Beef mixture onto the bottom halves of the toasted buns. Top with shredded Swiss cheese and place under the broiler for 1-2 minutes, just until the cheese has melted. Add the top buns, garnish with fresh thyme if desired, and serve immediately.