A semi-boneless rib roast is a cut of beef that has had the back bone removed, but the rib bones are still intact. It is also known as prime rib, and is a succulent, flavorful cut of meat that you don't need to fuss over for it to turn out tasty. The biggest problem with cooking this cut of beef is overcooking, so have a meat thermometer handy to keep an eye on the temperature the meat reaches.
Allow your roast to reach room temperature. This is important, as it allows the natural juices of the meat to redistribute and brings out more flavors. This will usually take about an hour for a 7- to 8-pound roast. Add 15 minutes to the standing time for each extra pound beyond seven. Do not allow your roast to sit at room temperature for more than two hours, however, as this will allow bacteria to grow and could pose a risk for food poisoning.
Preheat your oven to 500 degrees Fahrenheit. Add 1 cup each of diced carrots, celery and onion to a roasting pan. Season the vegetables well with salt and pepper. Place your rib roast on top of a rack in the roasting pan. Rub your roast with butter. Avoid using salt on the meat, as this will draw moisture out of the meat during cooking, which will produce a drier finished product.
Cook the meat at the maximum temperature for 15 to 20 minutes. This will sear the outside of the meat and lock the natural juices inside. Check the vegetables to see if they have begun to brown, and turn the oven temperature down to 375 degrees Fahrenheit. Pour beef broth or stock over the vegetables until covered.
Check your meat thermometer religiously during this process to ensure a perfectly cooked roast. When the internal temperature of the meat reaches 125 degrees Fahrenheit, take the roast out of the oven. Cover the pan with aluminum foil and let the meat rest for at least 20 minutes. This will allow carry-over cooking to bring the internal temperature of the meat up to 135 degrees Fahrenheit or a little more, which is medium rare. If you prefer your meat cooked longer, take the meat out when the internal temperature is 10 degrees less than the desired temperature. Medium will reach 150 degrees F., and well done will reach 165 degrees Fahrenheit.
Blend your vegetables together in a blender with a little bit of the juice while your meat is resting. Once the mixture has been blended well, add the rest of the juice and blend until smooth. Add corn starch to thicken the mixture if desired. Serve with the roast for prime rib and au jus.