Let the steak rest outside the refrigerator for 30 minutes before cooking. Use a hot, clean, oiled grill. If pan roasting, preheat the oven to 450 degrees F.
Liberally season the steak with the salt and pepper, coat with olive oil and press the seasoning into the meat. Grill the steaks for about 5 to 6 minutes on each side for medium rare. The fillet will cook a little faster than the strip loin. Move the steaks every 2 minutes or so for even cooking and a crispy exterior.
For pan roasting, heat a cast iron skillet with a little olive oil until smoking hot. Turn on the fan, open the window and stand back to avoid getting splattered! Using tongs, place the steaks in the center of the pan. Cook until the first side is seared brown, about 4 minutes. Turn the steaks and place the pan in the oven until the steaks are done, about 6 minutes for medium rare. Remove the steaks to a carving board and let rest for at least 5 minutes before carving.
Cut the steaks away from the bone and carve into 1/2-inch slices. Arrange the meat on warmed plates and drizzle a little bit of balsamic vinegar over the slices. Serve with some extra gray sea salt on the side.