Step 1: Prepare the Meat - Pound your slices of steak, veal, chicken, or turkey to 1/4 inch thickness for even cooking.
Step 2: Set Up Your Breading Station - In three shallow dishes, place the flour in one, the beaten egg in the second, and the panko breadcrumbs in the third. Season the flour with garlic powder, onion powder, kosher salt, and black pepper.
Step 3: Bread the Meat - Dredge each piece of meat in the seasoned flour, dip in the egg, and coat with panko breadcrumbs.
Step 4: Cook the Vegetables - In a large skillet over medium heat, add oil and sauté onions and bell peppers until softened, about 5-7 minutes. Add mushrooms and cook for an additional 3-4 minutes.
Step 5: Cook the Meat - In the same skillet, add more oil if needed, cook the breaded meat for about 3-4 minutes on each side until golden brown. Place a slice of cheese on each piece to melt in the last minute.
Step 6: Assemble the Sandwiches - Spread mayonnaise and grainy mustard on toasted hoagie rolls. Layer sautéed vegetables, cheesy meat, and top with the other half of the roll.