Bring a large skillet or sauté pan over medium-high heat and add the ground beef. Brown beef, breaking it up as it cooks. Once cooked, add the peppers and onions and continue to cook for a few more minutes until vegetables are softened. Mix in the steak sauce, beef broth, salt and pepper and bring to a bubble. Allow the mixture to bubble for about 5 minutes.

Make sure you have an oven rack in the top third of your oven and pre-heat the oven to broil. Line a baking sheet with aluminum foil. Open the sandwich rolls and lay both sides cut side up. Using your fingers, press the middle-inside of the bottom half of the roll to make a little more room for the meat mixture. Scoop about ¾ cup of the meat mixture onto the pressed bottom half of each roll. Top the meat mixture with a slice of the cheese. The top half of the rolls will be bare and cut side up.

Place the baking sheet onto the oven rack in the top 1/3 of the oven and broil for about 1 minute (check at 30 seconds and again at 50 to prevent burning – broiling happens fast!) Cover the loaded bottom half of each roll with its toasted top half counterpart and serve!