Place oven rack on lower level. Preheat oven to 450 degrees. Rub roast all over with salt and pepper. Transfer to heavy 13-by-16-inch metal roasting pan. Arrange fat-side up. Place short ribs in pan.
Cook 20 minutes. Reduce oven temperature to 325 degrees, and continue cooking until an instant-read thermometer inserted in the thick end of roast (not touching a bone) reaches 115 degrees, about 1 hour and 25 minutes. If it hasn't, return it to oven; check temperature at 10-minute intervals.
Transfer roast to platter; set aside in warm spot for juices to collect. (As roast rests, temperature will increase about 10 degrees.) Do not tent, or crust will get soggy. The short ribs can be eaten as a snack, or reserved to make flavorful soups.
Pour fat and all dark drippings out of pan into a fat separator; set aside.
Place roasting pan over medium-high heat. Pour red wine into pan; scrape bottom with wooden spoon, scooping up crispy bits to deglaze pan. Add the drippings that have settled to the bottom of the fat separator, making sure not to add the fat. Cook until reduced by half, 5 to 8 minutes. Place a fine sieve in a medium heatproof bowl. Pour juices into strainer. Using a wooden spoon, press down on solids to extract juices. Discard solids. Serve the juices warm with the prime rib.