Heat oven to 350˚F. Sprinkle shanks with salt. Heat oil in a large saute pan over medium-high heat. Add shanks to pan in batches until browned on all sides, about 5-7 minutes. Transfer shanks to a plate as they brown.

Drain all but 2 tablespoons of fat from the pan; add onions, carrots, celery, garlic, tomato paste, 1 teaspoon herbes de Provence and a light sprinkling of salt. Saute vegetables to soften them slightly, about 3-4 minutes. Add wine, then stock, stirring with a wooden spoon to loosen browned bits from the bottom of the pan. Bring liquid to a simmer, transfer vegetables and liquid to deep braising pan large enough to hold shanks in a single layer. Add shanks, season with salt, pepper and herbes de Provence.

Cover pan and transfer to oven. Braise shanks for 1 1/2 hours. Uncover and continue braising until shank tops are browned, about 30 minutes. Turn shanks and braise until other side is browned and shanks are fall-off-the-bone tender.

Remove pan from oven; let shanks rest for at least 15 minutes. Remove shanks from pan, skim excess fat from braising liquid and adjust seasonings. Spoon braising liquid over shanks and serve.