Prepare the Veal Shanks: Pat the veal shanks dry with a paper towel, season with salt and pepper, and dredge lightly in flour, shaking off excess.
Brown the Veal: Heat olive oil in a large skillet or Dutch oven over medium-high heat. Sear the veal shanks for 3–4 minutes per side until golden brown. Remove and set aside.
Sauté Aromatics: In the same skillet, add the chopped carrot, celery, onion, and garlic. Cook for 5 minutes until softened and fragrant.
Deglaze the Pan: Pour in the white wine, scraping up any browned bits from the bottom of the skillet. Let it reduce for 2–3 minutes.
Add Tomato Paste and Stock: Stir in the tomato paste and chicken stock, combining to form a rich braising liquid.
Braise the Veal: Nestle the veal shanks into the sauce, then add the bay leaf and rosemary sprigs. Cover and simmer on low heat for 1.5–2 hours, turning the veal occasionally. The meat is done when it’s tender and falling off the bone.
Make the Gremolata: Combine finely chopped parsley, garlic, and lemon zest in a small bowl to create a fresh, zesty garnish.
Serve: Plate the veal shanks, spoon the sauce generously over them, and sprinkle with gremolata. Pair with saffron risotto, mashed potatoes, or crusty bread.