Heat olive oil and butter in a large skillet over medium-low heat. Add sliced onions and cook slowly, stirring occasionally, until deeply golden and caramelized, about 20–25 minutes.,Increase the heat to medium. Add the ground beef and garlic to the skillet with the onions. Cook until the beef is browned and fully cooked, breaking it up with a spoon.,Stir in the Worcestershire sauce and sprinkle in the flour. Cook for 1–2 minutes to remove the raw flour taste.,Add the beef broth and thyme. Stir and simmer for 5 minutes until the mixture thickens and becomes saucy. Season with salt and pepper to taste.,Scoop the beef and onion mixture onto the bottom halves of the toasted buns. Top each with a slice of provolone or Swiss cheese.,Close with the top buns and serve warm.