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Place oven rack on lower level. Preheat oven to 450°F. Rub salt and pepper all over the roast.
Transfer to a heavy 13-by-16-inch metal roasting pan. Arrange fat-side up. Place short ribs in the pan.
Cook for 20 minutes. Reduce oven temperature to 325°F, and continue cooking until an instant-read thermometer inserted in the thick end of the roast (not touching a bone) reaches 115°F, about 1 hour and 25 minutes. If it hasn't, return it to the oven; check the temperature at 10-minute intervals.
Transfer roast to platter; set aside in a warm spot for juices to collect. (As the roast rests, the temperature will increase by about 10°F.) Do not tent, or the 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 the pan into a fat separator; set aside.
Place roasting pan over medium-high heat. Pour red wine into the pan; scrape the bottom with a wooden spoon, scooping up crispy bits to deglaze the 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 the strainer. Using a wooden spoon, press down on solids to extract juices. Discard solids.
Serve the juices warm with the prime rib.