Heat a large skillet over medium-high heat until scorching. Add the lean ground beef without stirring for the first minute to create a crust. Break apart and brown for about 5-7 minutes until fully cooked. Transfer to a plate and set aside, keeping the drippings in the pan.

In the same skillet, melt butter over medium heat. Add yellow onion, green bell pepper, and brown mushrooms. Sauté for about 5-7 minutes until golden and tender.

In a mixing bowl, combine beef broth, cornstarch, ketchup, Worcestershire sauce, kosher salt, and ground black pepper. Stir until mixed, then pour into the skillet with vegetables. Cook for a couple of minutes to marry flavors.

Allow the sauce to simmer for 3-5 minutes until thickened and glossy.

Return browned ground beef to the skillet. Mix well over low heat for about 2 minutes to combine flavors.

Off the heat, stir in slices of provolone cheese to melt into the mixture.

In another skillet, toast the brioche buns, buttered lightly, for 2-3 minutes until golden brown.

Spoon the cheesy beef mixture onto the toasted buns and serve immediately.