Preheat oven to 160°C/325°F. Sprinkle beef with salt and pepper. Heat fat in a large ovenproof pot over high heat. Add half the ribs and brown all sides. Remove and repeat with remaining ribs, then remove and set aside.
Turn the heat down to medium. Add shallots and garlic into the same pot and cook for 2 minutes. Add carrot and celery, and cook for 5 minutes until the carrot is softened and sweet. Add tomato paste and cook for 1 minute. Add wine, broth, thyme and bay leaves. Stir until tomato paste is dissolved.
Return beef into liquid, arranging them so they are submerged. Cover with a lid and transfer to the oven for 3 hours, or until the meat can easily be pried apart with a fork.
Remove beef carefully, keeping the meat on the bone. Cover with aluminum foil to keep warm. Strain all liquid in the pot, pressing juices out of the vegetables. Return liquid to the pot, bring to a simmer and stir until thickened, season with salt and pepper to taste.
Place beef on a warm serving plate, and spoon over the sauce. Serve!