Season the beef cutlets evenly with salt and black pepper.
Set up a breading station with three shallow dishes: place the flour in the first, the beaten eggs in the second, and the Panko breadcrumbs in the third.
Dredge each seasoned beef cutlet in the flour, dip into the beaten eggs, and coat thoroughly with the Panko breadcrumbs.
Heat the vegetable oil in a large skillet over medium-high heat until it reaches 350°F (175°C).
Fry the breaded beef cutlets for 3-4 minutes per side until they are golden brown and cooked through.
Transfer the fried cutlets to a paper towel-lined plate to drain.
Lightly toast the sub rolls. In a medium bowl, toss the shredded romaine lettuce with the Caesar dressing and grated Parmesan cheese.
Assemble the sandwiches by placing a crispy beef cutlet on each toasted sub roll and topping generously with the dressed romaine salad.