Pat the shanks dry with a paper towel and lightly salt and pepper.
Heat oil in heavy large Dutch oven over medium-high heat. Cook shanks until brown on all sides, about 8 minutes. Transfer to a plate.
Add onions, carrots, celery, and garlic to the pan and sauté until cooked through, about 10 minutes. Add tomato paste and cook stirring constantly for 1 – 2 minutes.
Stir in wine, tomatoes, and beef broth. Add the sprigs of rosemary and thyme.
Return shanks to pot, pressing down to submerge. Bring to a boil, and then reduce heat to medium-low. Cover and simmer 2 – 3 hours until the meat is tender.
Remove cover from pot. Simmer about 20 minutes longer. Transfer shanks to a plate and cover with aluminum foil. Boil juices about 15 minutes until thickened.
Serve shanks over creamy polenta and spoon the juices over the shanks.
