While your roast is resting, pour off all but 2 tablespoons of the fat from the pan and place on the stovetop over medium heat. Add the flour and cook, stirring, for 5 minutes to form a roux. Pour in the cold beef broth, slowly at first, whisking into the roux, add more broth and scrape all the caramelized beef drippings from the bottom of the pan.
Turn heat to high and cook the sauce for 10 minutes until it reduces and thickens slightly. This is not a gravy, so don't expect a thick, heavy sauce. Adjust seasoning, serve hot along side the prime rib.