- Adjust oven rack to lower-middle position and heat oven to 325 degrees.
- Heat 2 Tbsp of vegetable oil in large ovenproof Dutch oven over medium-high heat until smoking. Meanwhile, dry shanks thoroughly with paper towels, then season generously with salt and pepper. Place shanks in single layer in Dutch oven and cook until golden brown on one side, about 5 minutes. Flip shanks and cook on second side until golden brown, about 5 minutes longer. Transfer shanks to bowl and set aside.
- Off heat, add 1/2 cup white wine to Dutch oven, scraping bottom with wooden spoon to loosen any browned bits. Pour liquid into bowl with browned shanks.
- Return pot to medium heat, add remaining vegetable oil, heat until oil is shimmering. Add carrots, onions and celery and cook. Stirring occasionally, until soft and lightly browned, about 9 minutes. Add garlic and cook until lightly browned, about 1 minute longer.
- Increase heat to high and stir in broth, remaining wine, juices from veal shanks and bay leaves. Add tomatoes and veal shanks to pot (liquid should just cover shanks). Bring to simmer. Cover pot and place in oven. Cook shanks until meat is easily pierced with fork, but not falling off bone, about 2.5 hours.
Osso Buco may be prepared up to 3 days in advance and stored in an air tight container in the refrigerator. The meat should be stored and reheated in the braising liquid to prevent it from drying out. Scrape the chilled fat off the top and bring the osso buco to a simmer over medium-low heat in a covered Dutch oven, adding broth or water to adjust the consistency, if necessary.
This recipe can also be made with beef shanks and beef stock if desired.