Heat a few tablespoons of olive oil in a Dutch oven over medium-high heat until shimmering. Season the veal shanks generously with salt and pepper, then sear them in the hot oil for about 4-5 minutes on each side, until browned. Remove and set aside.

In the same pot, add the chopped carrots, onion, celery, and minced garlic. Sauté over medium heat for about 5-7 minutes until softened and fragrant.

Pour in a cup of dry white wine and simmer for about 2 minutes, scraping the bottom to deglaze. Add chicken broth, bay leaves, and thyme, stirring to combine.

Return the veal shanks to the pot, ensuring they're submerged. Cover and braise on low heat for approximately 2 hours until the meat is tender.

Prepare the gremolata by mixing parsley, lemon zest, and minced garlic in a small bowl.

Once tender, remove from heat and let it rest. Plate the veal shanks, spoon the braising liquid over them, and sprinkle gremolata on top before serving.