Begin by placing your thin slices of steak, veal, chicken, or turkey between two sheets of plastic wrap. Use a meat mallet to pound them to an even 1/4 inch thickness. This will ensure they cook quickly and remain tender.
In three separate shallow bowls, place the all-purpose flour in one, the beaten egg in another, and the panko breadcrumbs mixed with garlic powder, onion powder, kosher salt, and black pepper in the last bowl.
Dredge each piece of meat in the flour, shaking off any excess. Next, dip it into the egg, allowing any excess to drip off, and finally coat it in the panko breadcrumb mixture, pressing lightly to adhere.
In a large skillet over medium heat, add a drizzle of oil. Sauté the thinly sliced onions, bell peppers, and mushrooms until they are tender and caramelized, about 7-10 minutes. Season with a pinch of salt and pepper.
In the same skillet, add a bit more oil if needed and increase the heat to medium-high. Add the breaded meat and cook for about 3-4 minutes on each side, or until golden brown and cooked through.
Once the meat is cooked, place a slice of cheese on top of each piece and cover the skillet with a lid for about 1-2 minutes, allowing the cheese to melt.
Spread mayonnaise and grainy mustard on the toasted hoagie rolls. Layer the sautéed veggies on the bottom, then add the cheesy meat on top. Close the sandwich and enjoy!
