It's relatively easy to judge the doneness of a steak, either by watching the meat change color at the edge or by pressing it with a fingertip to assess its firmness. For a roast such as a ribeye, the larger size of the cut means those tactile and visual cues aren't available. Recipes typically provide a rough guide, based on weight and cooking time, but the only way to really know when your ribeye is perfectly cooked is by using a thermometer.
Trim any loose pieces of fat or connective tissue from the surface of your ribeye with a sharp knife. Look at the ends of the roast to see whether its shape is cylindrical or relatively flattened and oblong. An oblong roast cooks more evenly if you tie it tightly, approximately every 2 inches, with cotton butcher's twine. This makes it cylindrical so the heat penetrates the meat at the same pace from all directions.
Season the surface of the roast liberally with salt and pepper or with your choice of dry or paste flavorings. At this stage you can cook the roast immediately or cover and refrigerate it overnight so the flavors of your spice rub can mature and infuse into the meat.
Preheat your oven to 225 degrees Fahrenheit. Place the seasoned ribeye in your roasting pan and insert the probe of your thermometer into the middle of the thickest muscle. Slide the roast into your oven, positioning the thermometer's cable near the top of the oven door.
Plug the thermometer's probe cable into the display and power it up. Set your target temperature for 10 to 15 degrees below your preferred level of doneness. For example, if you want medium-rare beef at 130 to 135 F, set the thermometer to alert you when it reaches 120 F.
Slow-roast the ribeye until you're alerted by the thermometer's tone, roughly 3 to 4 hours, depending on the size of the roast. Double-check the roast's temperature with an instant-read thermometer, because the metal probe of a digital thermometer can conduct heat into the meat and report a temperature that's slightly higher than the rest of the roast.
Pull the roast from your oven and let it rest under a loose covering of foil for up to 30 minutes as its temperature rises to the desired doneness. Turn your oven up to its maximum temperature, usually 500 F, about 10 minutes before you're ready to serve the meal. Return your roast to the oven for 8 to 10 minutes; this browns the surfaces and creates rich, savory flavors. Transfer the roast to a serving platter and take it to the table.