Sprinkle short ribs all over with salt and pepper.
Add 6 ribs to flour mixture and turn to coat.
Heat 3 tablespoons oil in heavy large pot over medium-high heat.
Add floured ribs; saut) until brown, turning occasionally, about 6 minutes.
Transfer to large bowl. Repeat flouring and browning with remaining 6 ribs; reserve remaining flour-coating mixture.
Add 1 tablespoon oil to pot.
Add onions, carrots and celery stalks; saut) until vegetables begin to brown and are very tender, scraping bottom of pot often, about 30 minutes.
Add garlic, thyme and caraway seeds to pot; stir 1 minute.
Mix in tomatoes and bay leaves. Return ribs and accumulated juices to pot, arranging ribs in single layer.
Add broth and wine. Bring to boil. Reduce heat to medium-low, cover and simmer until meat is almost tender, about 1 hour.
Uncover pot. Simmer ribs 30 minutes, occasionally spooning fat from surface; reserve 2 tablespoons fat. Stir reserved flour-coating mixture and reserved 2 tablespoons fat in small bowl until smooth; mix paste into sauce around ribs. Simmer until meat is very tender and gravy thickens, about 45 minutes longer. Season with salt and pepper.