In a large skillet, melt a tablespoon of butter over medium heat. Add the thinly sliced onions and sauté them for about 8-10 minutes, stirring occasionally until they become caramelized and golden brown.

Push the onions to the side of the skillet, and add the ground beef. Use a spatula to break it apart while cooking. Season with salt and pepper to taste. Cook until browned and fully cooked through, which should take about 5-7 minutes.

Pour in the beef broth and sprinkle the onion soup mix over the meat. Stir everything together, allowing it to simmer for another 5-10 minutes to let the flavors meld.

While your beef mixture is simmering, butter the inside of each hamburger bun. Toast them on another skillet or under a broiler until golden brown.

Spoon the beef mixture generously onto the toasted buns. Top each sandwich with a good helping of shredded Swiss cheese.

Place the assembled sandwiches under the broiler for a couple of minutes until the cheese is melted and bubbly.

Take them out, allow to cool slightly, and serve with your favorite sides like coleslaw or potato chips.