Pat the beef shanks dry with paper towels to remove excess moisture. Secure the meat to the bone with kitchen twine. Season each shank with salt and pepper, then dredge them in flour, shaking off any excess.

Heat the olive oil in a Dutch oven over high heat. Once hot, add the beef shanks and brown on all sides, about 3 minutes per side. Remove the shanks from the pot and set aside.

In the same pot, add the diced onion, carrots, and celery. Sauté until the vegetables are translucent, about 5-7 minutes. Add the thyme sprigs, bay leaves, and canned tomatoes. Cook for 10 minutes, stirring occasionally.

Pour in the beef broth and return the beef shanks to the pot. Bring the mixture to a boil, then remove the pot from the heat.

Preheat the oven to 325°F (170°C). Cover the Dutch oven with a lid and transfer it to the oven. Braise for 2 hours, or until the beef is fork-tender.

Carefully remove the beef shanks from the pot. Cut off and discard the kitchen twine. Pour the sauce from the pot over the shanks and serve immediately.