Place the pan with the drippings in it on the burner over medium heat. There should be some juices and brown bits in the bottom of the pan. If there isn't any drippings, add 2 or 3 pats of butter to the pan and it will still pick up the flavor from the roasted meat.
Add the garlic, stir for a minute, then add the broth and the wine, bring to a boil, stir again, scraping up any brown bits from the bottom of the pan. Let it reduce slightly. Using a whisk, blend in the mustard, thyme,and add salt and pepper to taste.
Place the sliced meat on the platter or dinner plate, and ladle the sauce over it to serve, or furnish a small dish of sauce at each plate. We prefer it ladeled over ours.
If you prepare roast beef and some guests like their beef well done, here is how to give them what they like: Just lower their slice of prime rib into the pan sauce for about 15 seconds per side just until the red is gone, and remove to the dinner plate and and serve. The well-done meat will still be tender and juicy. Enjoy!
Cook's Tip: There is no need to thicken as this makes a wonderful pan sauce for beef wihtout the extra calories. However, it could be thickened as a gravy.
Update: Gotta share! We had the leftover Prime Rib for lunch. I heated the pan sauce and then lowered the cold meat into it and heated it up but made sure it didn't boil. I then put the hot slices of beef on top of a slice of french bread and ladled the pan sauce over the top. Open faced sandwiches! The only thing missing was mashed potatoes, and I think the pan sauce would have been great on those, too. It doesn't have to be thickened. (less calories!) It was the most delicious beef I have ever put in my mouth. No kidding. This is a keeper. I add this to my recipe so people will know there is a good way to use leftover prime rib or roast beef. Enjoy!