A bone-in ribeye roast is the same as a prime rib roast, a roast taken from the rib portion of beef, between the chuck at the front shoulder and the short loin on the back. This is one of the most prized beef cuts because it combines the tender qualities common in the loin with the beefy flavor common in the chuck. Bone-in ribeye roasts are commonly served whole with the rib bones sticking straight up and carved at the table, but you can also carve it beforehand to get the meat off the bones so it's easier to serve guests.
Remove the ribeye from the pan and set it on a carving board to rest for about 10 minutes, allowing the flavorful juices that retreat to the center while cooking to redistribute throughout the roast.
Lay the roast with the rib bones down on the cutting board and the ribeye meat facing up toward you. The rib bones should point in the direction of your dominant hand, so if you're right handed, point the bones to the right.
Slice the meat directly against the curved rib bones, leaving the bones bare and the rib roast meat in one large piece. Follow the curve of the bones, working from the side of your dominant hand to the opposite side. Cut it with a long carving knife so you can make clean, even cuts without a sawing motion. Save the rib bones for making beef stock or flavoring stew.
Position the meat lengthwise in front of you. Hold the roast steady with a meat fork in your non-dominant hand. Slice the meat into even slices anywhere between 1/2 inch and 2 inches thick. Consider the number of people you need to serve and the desired portion sizes when determining how thick to cut each slice.
Move the sliced ribeye meat to a serving plate, keeping the slices together as they were before cutting the roast. It helps to slide the knife under the meat and support it with your hand on top. Tilt the meat to one side and fan the slices out slightly so the juicy meat inside is visible.