Begin by pounding your chosen meat (steak, veal, chicken, or turkey) to about 1/4 inch thickness to fit the length of your hoagie rolls.
Set up a dredging station with three bowls: one with all-purpose flour seasoned with garlic powder, onion powder, salt, and pepper; one with the lightly beaten egg; and one with panko breadcrumbs. Coat each piece of meat in flour, then egg wash, then panko breadcrumbs.
In a large skillet, heat a tablespoon of oil over medium heat. Add the sliced onions, bell peppers, and mushrooms. Sauté for about 5-7 minutes until tender and slightly caramelized. Season with salt and pepper. Remove from skillet and set aside.
In the same skillet, add another tablespoon of oil if needed and heat over medium-high heat. Cook the breaded meat for about 3-4 minutes on each side until golden brown and cooked through. For chicken or turkey, ensure internal temperature reaches 165°F.
Once the meat is cooked, place a slice of Provolone or Swiss cheese on top of each piece. Cover the skillet for a minute to melt the cheese.
Spread mayonnaise and grainy mustard on toasted hoagie rolls. Place cheesy meat on bottom half, top with sautéed vegetables, then cover with the top half of the roll. Serve and enjoy!