In a large skillet heated over medium-high, add the lean ground beef and cook for about 1 minute without stirring, allowing it to brown nicely. Once browned, break apart and cook until no longer pink, about 4-5 minutes. Transfer beef to a bowl and set aside.

In the same skillet, reduce heat to medium and melt the butter until frothy. Add the chopped yellow onion, bell peppers, and minced mushrooms, sautéing for about 5-7 minutes until softened and golden brown.

Whisk together beef broth, cornstarch, ketchup, Worcestershire sauce, salt, and pepper in a bowl until smooth. Pour into the skillet with the cooked vegetables and stir well. Simmer for about 3-5 minutes until the sauce thickens.

Return the browned beef to the skillet, mixing well to combine all ingredients. Cook together for an additional 2-3 minutes over medium heat.

Turn off the heat and stir in provolone cheese until melted and creamy. Cover if you like gooey cheese.

Slice the brioche buns in half and spread butter on the cut sides. Toast them in a griddle or toaster oven at medium heat for about 3-4 minutes until golden brown.

Spoon the cheesy beef mixture into the toasted buns generously. Serve immediately, ideally with sweet potato fries or a salad.