In a large skillet, heat the olive oil over medium heat. Add the chopped onion and cook for about 5 minutes, or until softened and translucent.

Add the minced garlic and cook for an additional minute until fragrant.

Increase the heat to medium-high and add the ground beef to the skillet. Cook until browned, breaking it apart with a spatula, about 5-7 minutes. Drain any excess fat.

Stir in the beef broth, Worcestershire sauce, Dijon mustard, dried thyme, salt, and pepper. Bring the mixture to a simmer and reduce the heat to low. Let it simmer for about 10-15 minutes, allowing the flavors to meld and the sauce to thicken.

While the beef mixture simmers, preheat your oven to 350°F. Place the hamburger buns on a baking sheet and toast them in the oven for about 5 minutes.

Once the beef mixture is ready, spoon it generously onto the toasted buns. Top each with shredded Swiss cheese and return to the oven for an additional 5 minutes, or until the cheese is melted and bubbly.

Serve immediately and enjoy your delicious French Onion Beef Sloppy Joes!