Preheat oven to 325°F.
Remove visible fat from meat. Sprinkle ribs with a little salt and pepper. Heat 1 teaspoon oil in heavy large ovenproof pot or Dutch oven, over medium-high heat. Working in batches, add ribs to pot and brown well, turning often, about 8 minutes per batch. If your pan is large enough, brown all at once. Using tongs, transfer ribs to large bowl.
Pour off all drippings from pot. Add 1 teaspoon olive oil. Add onions, chopped carrot, and celery and cook over medium-low heat until vegetables are soft, stirring frequently, about 8 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 and any accumulated juices 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. After the first hour, add carrots and press carrots gently to submerge. Make one or two days ahead. Cool slightly, then refrigerate uncovered until cold. Cover and keep refrigerated. *The next day, remove the layer of fat that has formed on the top and toss.
Preheat oven to 350 degrees. About 30 minutes before ready to serve, bring to simmer on the stove top before continuing. Add remaining ½ cup broth and Kalamata olives to pot. Cover, return to oven and continue cooking at 350°F about 15 minutes, until heated through. Discard bay leaf. Transfer short ribs and carrots to platter. Tent with foil to keep warm. Pour sauce over short ribs.