Remove strip steaks from the refrigerator and transfer them to a clean plate. Salt both sides generously and keep them at room temperature for 45 minutes. About 15 minutes before cooking, preheat the grill to high heat
Brush olive oil on both sides of the steaks and sprinkle salt and pepper to taste. Transfer steaks to the grill, searing for 4-5 minutes on each side
Check that the internal temperature of the thickest part of the strip steak reaches 125-130 degrees for medium-rare. If necessary, grill for another 1-2 minutes over low heat for further cooking
Spread softened butter on a plate and place the cooked steaks on top. Tent the plate with foil and rest the steaks for 5-10 minutes before serving