Preheat oven to 325°F. Heat 2 tablespoons oil in heavy large oven proof
pot over medium-high heat. Sprinkle ribs with salt and pepper. Working in
batches, add ribs to pot and brown well, turning often, about 8 minutes.
Pour off all but 2 tablespoons drippings from pot or add oil as necessary to
measure 2 tablespoons.
Add onion, chopped carrot, and celery and cook over
medium-low heat until vegetables are soft, stirring frequently, about 10 minutes.
Add garlic, flour, and herbs de Provence; stir 1 minute. Add wine and 2 cups
broth; bring to boil over high heat, scraping up browned bits. Add tomatoes with
juices and bay leaf. Return ribs to pot. If necessary, add enough water to pot to
barely cover ribs. Bring to boil. Cover pot tightly and transfer to oven. Bake until
ribs are very tender, stirring occasionally, about 2 hours 15 minutes.
Add remaining 1/2 cup broth, peeled baby carrots, and Niçoise olives to
pot; press carrots gently to submerge. Cover, return to oven and continue
cooking at 350°F until carrots are tender, about 15 minutes. Discard bay
leaf. Transfer short ribs and carrots to platter. Boil sauce to thicken slightly.
Season to taste with salt and pepper. Pour sauce over short ribs. Sprinkle