These sandwiches originated in New York City and are traditionally made on a flat top grill; however, most people do not have those so I created a cast iron skillet version.
Combine mustard, ketchup, and cherry peppers in the bowl of a food processor. Pulse until smooth and set aside.
Melt butter in a small skillet over medium-high heat. Add onions and cook until onions are soft and are starting to caramelize, about 5 minutes. Remove from heat and set aside.
Form beef into two patties and season with salt and pepper. Heat a large cast iron skillet over medium-high heat. Add hamburger patties and cook 5 minutes or until a crust forms on the bottom. Flip patties over and cook 3 minutes.
Using a wide spatula, break patties up into large pieces. Sprinkle sauteed onion in between the spaces of the hamburger pieces. Layer cheese over the beef, and cook 2 minutes or until cheese is melted.
Spread reserved mustard sauce on the bottom bun of each hoagie roll. Divide meat mixture between the two sandwiches. Top each with shredded lettuce and sliced tomato.
Per Serving: 804 calories; protein 51.2g; carbohydrates 46.6g; fat 44.8g; cholesterol 173.4mg; sodium 1775.8mg.