Trimming the ribs from a rib roast might seem counterintuitive, but there are several good reasons for doing so. The resulting roast -- called a rib eye -- makes a less impressive appearance on the table, but it's easier to carve and it cooks more evenly. Although there are many ways to prepare a rib eye, it's traditionally served medium-rare in thick slices. The best way to achieve this goal is to roast the meat slowly at low temperature, then rapidly sear it at the end.
Trim any excess lumps or veins of surface fat from the roast, using the tip of a sharp knife. If the roast is flattened in shape rather than cylindrical, or if the butcher has cut into it deeply to remove a seam of fat, use cotton butcher's twine to tie it tightly into an even cylinder. This is optional, but rib eye roasts with a cylindrical shape cook more evenly than those left flattened.
Preheat your oven to 225 degrees Fahrenheit. While it's warming, season the roast liberally with salt and pepper or other flavorings as desired. Place the roast in a shallow roasting pan, preferably on a rack so air can circulate beneath it.
Slow-roast the rib eye for approximately 3 hours, depending on its size and your preferred degree of doneness. You'll need to take your roast out of the oven when it's still 5 to 10 F below the final temperature you want. For example, if you're attempting to reach a final temperature of 125 F to 130 F, or medium-rare, you should take it from the oven when an instant-read thermometer inserted into the middle of the roast reads approximately 120 F.
Adjust the racks in your oven, so the top of your roast will be about 4 inches from the broiler element when you re-insert the pan. Close the door, and turn on the broiler to preheat for 10 minutes. During this time your roast will rest, so you don't need to do it again later.
Slide the roast under your broiler until the top browns and sears, probably just a minute or two. Use long tongs to turn the roast so it browns on all sides, then remove it from your oven.
Carve the roast into thick slices and serve immediately, with your choice of side dishes.
You can use the same technique on your grill. Rake all the coals to one side of your grill, or light only one side of a gas grill, and bring the temperature to 225 F. Roast the beef under a closed lid on the side without direct heat, for the same length of time as for oven-roasting. Remove it from your grill when it reaches the correct degree of doneness and increase the temperature to 500 F. Sear the roast on all sides over the intense flame, then serve it.
If you have a remote probe thermometer, you can use that instead of an instant-read thermometer to judge the doneness of your roast. Bear in mind that the metal probe itself conducts heat into the beef, shortening cooking time in its own vicinity, and as a result it will likely read 3 to 5 degrees Fahrenheit higher than the true temperature.
If you buy a rib roast and cut off the ribs yourself, reserve them for another use rather than discarding them. The chewy meat between the bones becomes rich and tender when slow-cooked, or you can roast the ribs separately and use them to make gravy for your main roast.