1. Preheat oven to 350 degrees.
2. Heat 2 tablespoons of olive oil over medium heat in a pot large enough to hold all the veal shanks in a single layer.
3. Add the onion, carrot and celery.
4. Cook until the vegetables soften, about 10 minutes then drain the oil.
5. Meanwhile, heat the other 4 tablespoons of olive oil in a large saute pan over medium heat.
6. Dredge the veal shanks in the flour, coating on all sides and shake off the excess flour.
7. When the oil is hot, slip in the shanks and brown them on all sides.
8. Remove the veal shanks and place them in the pot on top of the cooked vegetables.
9. Drain all but a little bit of the oil from the saute pan that the shanks were browned in and add the wine.
10. Reduce the wine by simmering over medium heat while scraping loose the browning residues stuck to the bottom.
11. Pour the wine and pan juices over the veal shanks in the pot.
12. Add the butter, chicken broth, tomatoes, pepper and salt to the pot.
13. The liquid should come at least two thirds of the way to the top of the shanks.
14. If it does not, add more broth.
15. Bring to a simmer, cover the pot and place it in the oven. Cook for about 2 hours, turning and basting every 30 minutes, until the meat is very tender.
16. Transfer the ossobuco to a warm plate and carefully remove the strings.
17. Place a saucepan on a burner over high heat.
18. Pour the sauce from the pot into the saucepan through a strainer pushing as much of the vegetables through as you can with a wooden spoon. 19. If the sauce is thin and watery, boil it down until thickened, then pour the sauce over the ossobuco and serve.