Place the oil in a Dutch oven and heat over high heat. While the oil is heating, season the shanks with 1 1/2 teaspoons of the salt and 3/4 teaspoons of the pepper and dredge in the flour to coat. Shake to remove any excess flour. When the oil is almost smoking, add the shanks and cook until well-browned on both sides, about 4 minutes per side. Transfer the shanks to a plate and set aside. Add the pancetta, onions, celery, and carrots to the pan and cook, stirring occasionally, until vegetables are softened and lightly browned around the edges, about 4 minutes.
Add the garlic, bay leaves, rosemary, remaining salt, and remaining pepper and cook for 1 minute. Add the wine to the pan and stir to combine. Add the tomatoes and beef stock and return the shanks to the pan. Bring the cooking liquid to a boil, cover the Dutch oven, reduce the heat to medium low and cook, covered, for 2 1/2 to 3 hours, or until the shanks are very tender and beginning to fall away from the bones.
Using a slotted spoon, carefully transfer the shanks to a platter and cover with foil to keep warm. Skim as much of any accumulated fat from the surface of the cooking liquid as possible. Stir the parsley into the Dutch oven and continue to cook until the sauce thickens enough to coat the back of a spoon, about 10 minutes longer. Serve the shanks with polenta or risotto, drizzling the sauce over the shanks. Garnish with the grated Parmesan.
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