Place the compound butter on the counter and allow it to come up to room temperature for about an hour.
Light grill and set up for high direct heat. You’ll want to get the coals as hot and as close to the cooking grate as possible. If using a gas grill, allow the grill to preheat with the lid closed for at least 15 minutes.
Evenly coat strip steaks with olive oil and season them liberally with kosher salt. Put one pat of compound butter on each plate and set aside.
Place steaks directly over hot coals and flip every 30 seconds. With each flip, place the steaks in a different spot on the grill grate. This allows the best searing to take place through conductive heat.
After about five minutes of total cook time, use a reliable quick-read thermometer to check the internal temperature of the steak. Remove steaks from the grill when the internal temperature reaches 120°F for a medium rare steak.
Place steaks directly on top of butter pats, and add additional pat to top of steaks before tenting them with aluminum foil. Allow them to rest for five minutes. Carry-over cooking will continue, and the final serving temperature of the meat will be in the neighborhood of 127°F or so, the perfect medium rare.