Tomahawk is simply a rib-eye with most of the rib bone left intact. Tomahawk has a rich and buttery flavour, with a soft and succulent texture. Using a barbecue is a great way to cook your tomahawk. Pre-heat the BBQ to hot, and sear the steak on all sides, including the edges. Lower the temperature to medium (if a gas barbecue), close the hood and cook for 15-20 minutes.