Trim excess fat from steaks, rinse meat in cold water, and pat dry. Rest on counter until near room temperature. Tie steak with kitchen string and secure tightly. Massage with oil and seasoning liberally across surface of the ribeyes. Rest on counter for 15-20 minutes before grilling.
Preheat grill using the two-zone method by turning burners on one side of the grill to high while leaving the other side off. With grill lid open, lay steaks over hottest grill grates and sear 3-4 minutes per side. When charred upon both sides, turn down all burners to low and transfer steaks to the coolest grates. Top the steaks with a dollop of salted butter and close the grill lid. Remove steaks from grill when within 5 degrees of desired internal temperature in thickest part of the steak (ie. to prepare a medium-rare steak at 135F, remove from grill at 130F). Pull steaks from grill, loosely tent with tin foil for 5-10 minutes and allow carry-over energy stored in the steaks to finish the cook.
To plate, remove the kitchen string and slice the steak in 1/2" cuts across the grain and on a bias. Plate the steak alongside chared hearts of romaine salad, roasted lemon and garlicky hasselback potatoes. Garnish with fresh herbs and serve.