Start by heating your large skillet or griddle over medium-high heat with a little oil until it shimmers. Toss in your chopped onions and mushrooms immediately and spread them out in an even layer. Cook them down until they are deeply golden brown and smell sweet, which usually takes about five to eight minutes.
Push your caramelized vegetable mixture to the outer edges of the pan to create a hot center zone. Drop your ground beef right into the middle of the hot skillet and let it sit undisturbed for a minute. You want the bottom to develop a dark, flavorful crust before you start moving it around.
Using the sturdy edge of your wooden spatula, begin breaking the beef apart with a firm chopping motion. Keep chopping and flipping the meat repeatedly until it is no longer pink and is broken into small, pebbled bits. This specific texture is the signature of the sandwich, distinct from a standard burger patty.
Once the beef is fully browned and crispy, sprinkle salt, pepper, and your chopped cherry peppers over the meat. Mix the caramelized onions and mushrooms back into the beef from the sides of the pan. Stir everything together vigorously so the flavors of the vegetables and the heat of the peppers meld with the beef fat.
Gather the meat mixture into two separate rectangular piles roughly the shape and length of your bread rolls. Layer the American cheese and Provolone slices directly on top of each meat pile to cover them completely. Let it sit for a minute or two until the cheese is fully melted and bubbling into the meat crevices.
Give the cheesy meat mixture one final stir to incorporate the cheese throughout the beef like a sauce. Scoop a generous portion of the mixture directly onto your warmed or toasted hero rolls. Press the sandwich closed gently to let the bread absorb some of the delicious juices before serving.