Heat butter in a large skillet over medium heat. Add finely chopped onion and green bell pepper. Cook for about 3-4 minutes, letting them soften and release a wonderful aroma. Toss in the minced garlic and sauté for an extra minute.
Push the veggies to one side of the skillet and add your ground beef. Use a spatula to break it into small crumbles as it cooks. Season with salt and pepper. Cook until fully browned and no pink remains.
Sprinkle flour over the beef and veggie mixture. Stir well until the flour is no longer visible, helping to thicken the mixture. Then, pour in beef broth, ketchup, and Worcestershire sauce. Stir everything together and let it simmer for 5-7 minutes until it turns rich and saucy. Pro tip: Add extra broth if it thickens too much!
Reduce the heat to low and sprinkle shredded provolone cheese over the beef mixture. Cover the skillet and allow the cheese to melt into gooey perfection. Mix it lightly to combine.
Scoop the mixture onto the bottom halves of lightly toasted hamburger buns. Top with other half and serve hot! Add more cheese or sautéed mushrooms if you’re feeling fancy.