This wonderful recipe for braised short ribs is courtesy of chef Scott Conant. This recipe is a great dish to serve on its own but also serves as a great filling for Scott Conant's Short-Rib Ravioli.
Heat oven to 300 degrees. Season ribs with salt and pepper. In a Dutch oven, heat olive oil over medium-high heat. Sear ribs, in batches if necessary, until browned all over, 10 to 15 minutes. Remove ribs, and transfer to a large bowl; set aside.
Add carrot, celery, onion, and garlic to pot, using more olive oil if necessary; saute until browned, about 10 minutes. Add vinegar and red wine; stir with wooden spoon until all browned bits have been scraped from the pan and the bottom of the Dutch oven is clean. Continue to cook until liquid is reduced by 1/3. Add tomatoes, chicken reduction, and herbs. Return ribs to pot, bring to a boil, cover pot, and transfer to oven. Cook, turning ribs once or twice during cooking, until fork tender and meat is just barely clinging to the bone, 3 1/2 to 4 hours.
Remove ribs from pot; set aside. Strain, reserving cooking liquid, discarding solids. Use a large spoon to remove clear fat floating on surface of cooking liquid. Cook over medium-high heat until reduced and thickened.
Slice meat off ribs, against the grain, into 1/3-inch-thick pieces; ribs may be served whole, if desired. Serve drizzled with sauce.