Gather all your ingredients so that you have everything close at hand on the counter or table.
Prepare the Ingredients
Using a cutting board and a Santoku knife, slice the round steak into thin strips.
With a Chef's knife on a second cutting board, slice sweet onion, green bell peppers, and mushrooms. Mince the garlic.
Using a box grater, shred the mozzarella and provolone cheese. Set aside until ready to use.
Make the Steak Sandwich
In a large skillet, saute the sliced sweet onion, green bell pepper, mushrooms, and minced garlic in olive oil until tender and onions have caramelized. Season with kosher salt and freshly ground black pepper. Remove from pan and keep warm in a bowl.
With the same skillet, and using more olive oil, if needed, cook the prepared strips of steak on medium-high heat until brown. Sprinkle with more kosher salt and freshly ground black pepper.
Remove from heat. Cover the steak with the grated cheese and allow it to melt.
Toast the hoagie rolls in the oven or in a toaster oven until lightly browned.
To make the sandwiches, pile spoonfuls of cheesy meat on toasted rolls, then top with generous amounts of the onion mixture. Makes 4-6 sandwiches.