Flatten the chicken breasts to an even thickness using a meat mallet.
Set up a breading station with three shallow dishes: one with flour seasoned with salt and pepper, one with beaten eggs, and one with a mixture of breadcrumbs and Parmesan cheese.
Coat each chicken breast in flour, dip in egg, and then dredge in the breadcrumb mixture.
Heat oil in a large skillet over medium heat. Fry the chicken until golden brown and cooked through, about 4 minutes per side.
Preheat your oven to broil. Open the hoagie rolls and place them on a baking sheet.
Place a fried chicken breast on each roll and top with marinara sauce and two slices of mozzarella cheese.
Broil the sandwiches open-faced just until the cheese is bubbly and golden, about 3-4 minutes.
Close the sandwiches, slice in half, and serve hot.