Tender, fall-off-the-bone veal shanks braised in white wine, tomatoes, and aromatic vegetables until melt-in-your-mouth perfection. Topped with bright gremolata, this Milanese classic is the ultimate special-occasion meal.

Tie kitchen twine around the circumference of each veal shank to help them hold their shape during cooking. Pat the shanks dry with paper towels and season generously on both sides with 1 teaspoon salt and 1/2 teaspoon black pepper. Place 1/2 cup flour in a shallow dish. Dredge each shank in flour, shaking off any excess. Heat 3 tablespoons olive oil in a large, heavy-bottomed Dutch oven or braising pan over medium-high heat. Working in batches if needed, sear the veal shanks for 3-4 minutes per side until deeply golden brown on all sides. Transfer to a plate and set aside.
Reduce heat to medium. In the same pot, add 2 tablespoons butter. Once melted, add 1 diced onion, 2 diced carrots, and 2 diced celery stalks (the classic Italian soffritto). Cook for 6-8 minutes, stirring occasionally, until the vegetables are softened and lightly caramelized. Add 4 cloves minced garlic and cook for 1 minute until fragrant. Scrape up any browned bits from the bottom of the pot.
Pour in 1 cup dry white wine. Increase heat to medium-high and let the wine simmer for 3-4 minutes, scraping the bottom of the pot, until reduced by half. Add 1 can diced tomatoes (with their juice), 2 cups beef or veal stock, 2 bay leaves, and 3 sprigs fresh thyme. Stir to combine and bring to a simmer.
Return the seared veal shanks to the pot, nestling them into the braising liquid. The liquid should come about halfway up the sides of the shanks—add more stock if needed. Bring to a gentle simmer, then cover the pot with a tight-fitting lid. Reduce heat to low or transfer the covered pot to a preheated 325°F (165°C) oven. Braise for 2 to 2.5 hours, turning the shanks once halfway through, until the meat is extremely tender and falling off the bone. Check occasionally and add more stock if the liquid level drops too low.
While the osso buco finishes braising, make the gremolata. In a small bowl, combine the zest of 1 lemon, 1/4 cup finely chopped fresh parsley, and 2 cloves minced garlic. Mix well and set aside. This bright, fresh garnish is traditional and essential.
Remove the osso buco from the pot and place on a serving platter. Discard the kitchen twine, bay leaves, and thyme sprigs. Skim any excess fat from the surface of the braising liquid. If the sauce is too thin, simmer it uncovered over medium-high heat for 5-10 minutes to reduce and thicken. Taste and adjust seasoning with salt and pepper. Spoon the sauce and vegetables over the shanks. Sprinkle generously with gremolata. Serve immediately with risotto alla Milanese, creamy polenta, or mashed potatoes.
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