Prime Rib
Method
1 Remove roast from the refrigerator (still wrapped) a couple hours before cooking. Roasts should always be brought to room temperature first, before they go in the oven.
Cookbooks often call for the excess fat to be removed. By "excess" fat they mean any fat more than an inch thick. The fat is what provides the flavor and what you are paying for with prime rib, so you want to leave it on. Your butcher should have removed any excess fat.
2 Preheat your oven to 500°F, or the highest it will go (our oven only goes up to 450°F). Salt and pepper the natural fat covering the roast.

3 Insert a meat thermometer into the thickest part of the roast, making sure it doesn't touch a bone. (Some meat thermometers require that you poke a hole first with a skewer, and then insert the thermometer.) Place the roast, fat side up, rib side down in a roasting pan in the oven.
4 After 15 minutes on 500°F, reduce the heat to 350°F. To figure out the total cooking time, allow about 13-15 minutes per pound for rare and 17-20 minutes per pound for medium rare. The actual cooking time will depend on the shape of the roast and your particular oven. A flatter roast will cook more quickly than a thicker one. So make sure to use a meat thermometer. This is not a roast to "wing it". Error on the rare side.
Roast in oven until thermometer registers 120°F. for rare or 135°F. for medium.
Check the temperature of the roast using a meat thermometer a half hour before you expect the roast to be done. For example, with a 10 pound roast, you would expect 2 1/2 hours of total cooking time (15 minutes at 500° and 2 1/4 hours at 350°). In this case, check after 2 hours of total cooking time, or 1 hour 45 minutes after you lowered the oven temp to 350°.
Once the roast has reached the desired internal temperature, remove it from oven and let rest 30 minutes, covered with aluminum foil, before carving. The roast will continue to cook while it is resting.

5 With a knife or scissors, cut the strings which attach the meat to the bones. Remove the bones (save for making stock for soup. Then, using a sharp carving knife, slice meat across the grain for serving, making the slices about 1/4-1/2 inch thick.
Making gravy
To make the gravy, remove the roast from the pan. Place pan on stove on medium high heat. Pour off all but 2 tablespoons of the drippings to a separate container. Into the 2 tablespoons of drippings in the pan stir in 1 to 2 tablespoons of flour. Stir with a wire whisk until the flour has thickened and the gravy is smooth. Continue to cook slowly and stir constantly. Slowly add back the previously removed drippings (remove some of the fat beforehand if there is a lot of fat). In addition add either water, milk, stock, cream or beer to the gravy, enough to make 1 cup. Season the gravy with salt and pepper and herbs. (See also How to Make Gravy.)
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