Brown beef in a large skillet over medium-high heat for 6 to 7 minutes, breaking it into small crumbles. Transfer to a bowl and leave about 1 tablespoon fat in the skillet.
Cook onion, pepper and mushrooms in the skillet for 8 to 10 minutes until softened and the mushroom liquid evaporates. Return the beef.
Whisk broth, Worcestershire, mustard and cornstarch until smooth, then stir into the skillet with salt and pepper. Simmer for 3 to 4 minutes until glossy and thick, with the beef at 160°F.
Toast the split rolls. Lay provolone over the hot filling, cover the skillet and remove from the heat for 1 minute until the cheese softens.
Scoop the filling and melted cheese into the rolls and serve promptly.