1. In a large skillet over medium heat, add butter and olive oil. Once melted, add the sliced onions and cook slowly, stirring occasionally, for about 20 minutes until golden and caramelized.

2. Push onions to one side of the skillet and add ground beef. Cook until fully browned, breaking it up with a spoon as it cooks.

3. Stir the onions and beef together. Add minced garlic, Worcestershire sauce, and pour in the beef broth. Simmer for 5–7 minutes until slightly thickened.

4. While the meat simmers, toast the brioche buns in a skillet or under a broiler until golden and crisp on the inside.

5. Scoop generous portions of the beef-onion mixture onto each bun, top with provolone cheese, and briefly broil or torch to melt the cheese. Serve hot.