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Set oven rack to lower-middle and heat oven to 325 F.
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Pat dry each veal shank and tie around its center with kitchen twine, then season with salt and pepper.
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Heat 2 tablespoons of oil in a large ovenproof Dutch oven over medium-high heat, until the oil is shimmering. Place 3 shanks in the pan and cook until they are golden brown on one side, about 5 minutes. Carefully flip the shanks and cook on the second side until golden brown, about another 5 minutes. Transfer them to a bowl and set aside.
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Take the Dutch oven off the heat and add 1/2 cup of white wine, scraping the pan bottom to loosen any browned bits. Pour this liquid into the bowl with the browned shanks.
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Return the Dutch oven to heat, and 2 more tablespoons oil, and repeat this entire process with the next 3 shanks.
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With all shanks resting in a bowl off the heat, return the Dutch oven to heat, add 2 more tablespoons olive oil and bring up to medium-high heat again. Then add the carrots, onions and celery and cook until soft and lightly browned, about 10 minutes. Add the garlic and cook for another minute longer.
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Increase the heat to high and stir in the chicken broth, the rest of the white wine, any juice from the veal bowl, and the bay leaves. Then add the tomatoes and return the veal to the pot. Bring the this to a full simmer, then cover, crack the lid slightly, and move to the preheated oven.
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Cook the shanks until the meat is easily pierced with a fork, about 90 to 100 minutes.