1In large skillet over medium-high heat add the oil and then brown the ground beef, about 5-6 minutes.
Add the onion and green pepper and cook another 3-4 minutes, until the vegetables start to get tender. Stir in the steak sauce and beef broth, season with salt and pepper, bring up to a bubble and cook about 2 minutes.
2Split open rolls and remove most of the soft insides, leaving a bed to hold the meat mixture. Toast the rolls and set aside.While the meat is cooking, melt the butter in a medium-size pot over medium-high heat. Stir in the flour and cook about 1 minute. Whisk in milk, bring up to a bubble and let thicken, about 2 minutes. Turn off heat and stir in the cheese.
3To serve, place a scoopful of the meat mixture onto the bottom of the rolls, then top with the cheese sauce and replace the top of the roll.