Brown the Beef: Heat a large skillet over medium-high heat. Add the lean ground beef and sear for about one minute without stirring. Break it up and continue cooking until browned thoroughly. Remove and set aside.

Sauté the Vegetables: In the same skillet, melt a tablespoon of butter over medium heat. Add the diced yellow onion, green bell pepper, and brown mushrooms. Cook for 5-7 minutes until softened and golden.

Prepare the Sauce: In a mixing bowl, combine beef broth, cornstarch, ketchup, Worcestershire sauce, kosher salt, and ground black pepper. Whisk until smooth.

Combine Ingredients: Pour the sauce mixture into the skillet with the sautéed vegetables. Stir and let it come to a gentle boil for about 3-5 minutes. Return the browned beef and mix well.

Finish with Cheese: Remove from heat and stir in the chopped provolone cheese until melted and creamy.

Prepare Buns: Butter the insides of each brioche hamburger bun. In a separate skillet, toast the buns for 2-3 minutes until golden.

Assemble: Load the toasted buns with the cheesy beef mixture and serve immediately.