Preheat broiler to low. In large skillet over medium-high heat brown the ground beef about 5-6 minutes. Add the onion, green pepper, and mushrooms and cook another 3-4 minutes, until they start to get tender.
Stir in the steak sauce and beef stock, season with salt and pepper. Bring up to a low boil and cook for about 2 minutes.
Open buns and place on a baking sheet. Place a slice of cheese on the top half of each bun and put pan in the broiler. Broil for 1-2 minutes, or until cheese is melted and buns are golden brown.
Place a scoopful of the meat on the bottom half of the bun, drizzle with additional steak sauce and place cheesy bun on top.
Notes
If you want to substitute the provolone cheese, here are a few different cheeses that we would recommend:
Cheese Whiz – this is what they use on authentic Philly Cheesesteak Sandwiches!).