• Remove your prime rib from the refrigerator 1-2 hours before cooking. Sprinkle it with salt all over and let it sit, loosely wrapped in plastic wrap or butcher paper. Roasts should be brought close to room temperature before they go into the oven to ensure more even cooking.
• Preheat oven to 500°F/260°C.
• Mix together the butter, garlic, herbs, salt, and pepper in a bowl until evenly combined.
• Pat the roast dry with paper towels. Then rub the entire outside of the prime rib with the herb butter mixture.  Place roast fat side up in pan. A bone-in roast will have the bones down (the bones act as a rack), and a boneless roast should go on a rack.

  Insert an ovenproof meat thermometer into the thickest part of the roast, making sure that the thermometer isn't touching a bone.
  
• Bake prime rib at 500° for 15 minutes, then reduce the oven temperature to 325° and continue baking until desired doneness: 

  Rare: cook until thermometer reaches 120°F (about 10-12 min/pound)

  Medium rare: Cook until thermometer reaches 130°F (about 13-14 min/pound)

  Medium: Cook until thermometer reaches 140°F (about 14-15 min/pound)

  Medium well – Cook until thermometer reaches 150°F

  Be sure to go by temperature, not time, as the cooking time will depend on many variables like the size of your prime rib, your oven, how chilled the roast is when it goes in the oven, a flatter roast vs. thinner roast, etc. We can't emphasize this enough, use your meat thermometer and rely on it for the desired doneness!

  If you have a remote thermometer, it can tell you when the roast has reached the desired doneness. If you don't, check the roast about 1-hour before you think it should be done.

  For example, with a 10 pound roast, expect 2 hours of total cooking time for rare (15 minutes at 500° and 1 3/4 hours at 325°)
  
• Once the roast has reached the temperature you want, remove it from the oven and place it on a carving board. Cover it with foil and let it rest for 15 to 30 minutes before carving. The internal temperature of the roast will continue to rise while the roast is resting.

To Make the Gravy

• Remove roast from pan. Pour fat from the roasting pan. Then, pour the drippings from the pan into a saucepan.
• Add the flour, whisking until there are no lumps, then add the beef stock, stirring and bringing the sauce to a boil.
• Remove from heat and strain the sauce into a gravy dish.
• Carve the roast into thick slices, 3/4 inch. Serve with the sauce as gravy.