A day on the ranch is sure to build up a cowboy-sized appetite, but a thick, cowboy-cut ribeye doesn't come with a 10-gallon hat prerequisite. Typically cut to 2 1/2 inches thick, a cowboy-cut ribeye is basically the same as a bone-in ribeye steak, but the extra-large size and large, handle-like bone set it apart from its lightweight counterparts. This thick steak requires a longer cooking time to achieve the desired level of doneness, which means cooking at a lower temperature so the crust doesn't burn. The same basic principles apply whether you cook it on the grill or stove top.
Season the steak liberally on all sides with your choice of seasonings and spices. While you might prefer to skip marinades and spice rubs, the cowboy-cut ribeye will benefit from a generous sprinkling of salt either immediately before cooking or 40 minutes beforehand. Salt helps bring out the flavor of the steak and aids in retention of juices.
Preheat your skillet or grill to low or medium-low heat. Add a bit of oil to the skillet to prevent sticking, particularly if the skillet doesn't have a non-stick surface.
Set the steak in the preheated skillet or on the grill. Flip the steak about once every 5 minutes to heat the inside faster and more evenly. It can take up to 30 minutes for the inside to reach medium doneness, roughly 125 degrees Fahrenheit.
Insert a meat thermometer into the thickest part of the steak to check the temperature. Remove the steak from the pan or grill when it's about 10 degrees shy of the desired internal temperature. Rare steak is roughly 115 F; medium-rare is 120 F; medium is 125 F to 130 F; medium-well is between 130 F and 135 F; well done is 140 F. To cook a medium-rare steak, remove the steak when the internal temperature reaches 110 F.
Turn the heat up to high while allowing the steak to rest. The steak's internal temperature will rise about 5 degrees during the resting period, so it only needs to be brought up another 5 degrees. If using a skillet, a drop of water dropped in the pan should sizzle and evaporate almost immediately to indicate it is preheated properly.
Place the steak back in the skillet or on the grill and cook it for about 2 minutes on each side to develop a rich, brown crust on the outside. Lift the edge of the steak with tongs to check the color. The hot temperature browns the outside quickly without overcooking the inside. If you want a medium steak, for example, you'll have a pink center throughout without the undesirable, overcooked gray meat between the crust and center.
Remove the steak to a serving plate and allow it to rest for about 3 minutes. Given the extra time in the skillet or on the grill, plus the resting period, the steak should rise the extra 5 degrees to the desired level of doneness.