Pat beef dry. Heat oil over medium-high heat in a heavy-bottomed pot and brown beef on a ;l sides and remove. Reduce heat to medium and sauté carrot and onion until onion is translucent, about 5 minutes. Add garlic and sauté minute more. Add tomatoes, wine, stock, thyme and bay leaves and return to a simmer. Return beef to pot, cover and place in oven. Cook shortribs for 4 hours, adding vinegar after 2 hours until flesh pulls easily away from the bone. Before serving, stir in figs and season to taste.