Toss the romaine with 2 tbsp of olive oil, salt and pepper.
Season steaks with salt and pepper.
Put the steaks and romaine, flat side down on the grill. Grill steaks to preferred doneness, for medium-rare about 5 minutes preside until 130F. Char the romaine on the hot part of the grill until starts to weep but is still crunchy.
Remove steaks and romaine from grill. Allow the steaks to rest for about 5 minutes.
While steaks are resting, heat a sauté pan with 3 tbsp of oil and fry the over-easy eggs.
To assemble, rub the grilled romaine with dressing. Now place on the plate, sprinkle with parmesan and croutons. Top with eggs and serve with the steak.