Remove steaks from the refrigerator. Season generously on both sides with salt and let rest at room temperature for 45 minutes.
Brush grill grates with olive oil. Heat one area of the grill to high (you can use a charcoal or gas grill).
Season steaks with additional salt, if desired, and pepper and thyme.
Place steaks on the hottest side of the grill, searing for 3-4 minutes. Use tongs to flip the steaks to the other side and sear for another 3-4 minutes.
Move tomahawk steaks to a low-heat area of the grill to continue cooking until they reach your desired internal temperature, usually between 10-20 minutes. Remove from heat when a digital thermometer reads 120-125 degrees for medium-rare, and adjust accordingly for other doneness levels.
Rest at room temperature on a plate tented with foil for 5-10 minutes before serving.
