Season short ribs with salt, pepper and rub with tomato paste and dredge in flour. In a heavy-bottomed pan, sear short ribs in oil on all sides; transfer to ovenproof pan. Brown onions, carrots and celery, deglaze with wine; add vegetables, remaining wine, beef stock and thyme to pan with ribs, cover by three-quarters. Cover pan with foil; place in 325°F oven for 3 hour, cook until meat is falling off bones. Uncover and cool for one hour. Remove ribs from cooking liquid; strain and degrease liquid. Remove bones, excess fat and cartilage from ribs; place meat in bowl and shredded. Add barbecue sauce and the reserve liquid as need to keep moist. Place in a container and cool down. Yields 4 cups.