1. Preheat oven to 400 degrees. Place flour in a medium bowl; season with salt and pepper. Toss ribs in flour mixture until well coated; shake off excess.

2. In a 5- to 8-quart Dutch oven or heavy ovenproof pot, heat oil over medium-high. Cook ribs in two batches, turning until browned on all sides, about 10 minutes per batch; transfer to a plate.

3. Add carrots and onions to pot. Cook, stirring and scraping up browned bits, until vegetables are lightly browned, 3 to 5 minutes. Add wine, broth, thyme, and tomatoes (breaking them up). Arrange ribs in pot; bring liquid to a boil. Cover, transfer to oven, and cook 1 hour. Reduce heat to 350 degrees; cook until fork-tender (but not falling apart), about 1 hour more.

4. Using tongs or a slotted spoon, transfer ribs to a plate. Moisten with cooking liquid; cover with aluminum foil to keep warm. Strain remaining liquid through a fine-mesh sieve (discard solids); return to pot. Bring to a boil; cook until sauce is slightly thickened and reduced to about 2 cups, 10 to 12 minutes. Season with salt and pepper. Serve ribs with sauce. (Or return to pot, let cool slightly, cover, and refrigerator up to 1 day.)