Add 1 tablespoon of butter to a large frying pan over medium-low heat and cook the onions until well browned, which takes about 20 minutes. Set them aside.
Add 2 tablespoons of butter to a large frying pan and cook the peppers and mushrooms over medium-low heat until browned, which takes about 10 minutes. Set aside.
Season the ribeye steaks well with salt and pepper on both sides and cook on a hot grill or in a grill pan with 2 tablespoons of olive oil until grill marks have formed and the desired internal temperature is achieved. It will take about 2 to 3 minutes per side for a medium-rare internal temperature.
Divide the cooked sliced ribeyes between the 4 sliced hoagie buns and layer each sandwich with 2 slices of mozzarella cheese, 1 slice of provolone cheese, roasted onions, peppers, and mushrooms.
Add the sandwiches to the middle rack of the oven and cook for 5 minutes or until the cheese is melted and the bun is lightly toasted.
Serve the hot sandwiches along with the aioli.
Notes
Make-Ahead: This steak sandwich is meant to be eaten as soon as it’s done cooking. If you keep the sauce, veggies, mushrooms, and beef separate, you can make this up to 2 days ahead of time.How to Store: It is best to cover the sauce, cooked beef, bread,veggies, and mushrooms separate. If it is already assembled, cover it with plastic and keep it in the refrigerator for 3 days. This recipe will not freeze well.How to Reheat: Place the desired number of sandwiches on a sheet tray lined with parchment paper and bake them in the oven at 350° for 8 to 10 minutes or until warm. If you kept the main components of the dish separate, follow the procedures of the recipe for reheating.The beef in my recipe is seasoned and seared to a perfect medium-rare, but of course, you can cook it longer should you desire a more cooked-through internal temperature.