1. Place the mushrooms in a small bowl and cover with the boiling water. Soak for at least 45 minutes, or up to several hours. Remove the mushrooms from the liquid with a slotted spoon. Chop and set aside. Strain the soaking liquid, leaving behind any grit in the bottom of the bowl, and set aside.
2. Preheat the oven to 325F 3. Tie each shank with 3 loops of butcher's twine. Generously season the shanks with light salt and pepper. Heat 2 tablespoons of the oil in a large Dutch over over medium-high heat. Add the shanks (you may have to brown them in batches) and sear until nicely browned on all sides, about 10 minutes. Set aside the shanks and pour off all but 2 tablespoons of the fat. 4. Reduce the heat to medium and add the prosciutto, onions, carrots, celery, and leeks. Cover and cook until soft, stirring occasionally, about 10 minutes. Scrape up any browned bits from the bottom of the pot. Add the garlic, reserved mushrooms, and white wine and bring to a boil, scraping up any remaining browned bits from the bottom. Add the reserved mushroom liquid, the stock, 1 teaspoon of the rosemary, and the shanks. Bring to a boil. 5. Cover and bake for 30 minutes, then turn the shanks, re-cover the pot, and bake for another 30 minutes. Remove the lid and, after another 30 minutes, begin checking the shanks, adding more stock or water if the liquid evaporates. The shanks are done when the meat is almost falling off the bone and is quite tender. 6. Transfer the pot to the top of the stove and transfer the shanks to a shallow roasting pan. Increase the oven temperature to 425F. Brush the shanks with the remaining 1 tablespoon of olive oil and sprinkle with some pepper and the remaining 2 teaspoons of sage and 1 teaspoon of rosemary. Roast the shanks in the over for 15 to 20 minutes, or until slightly browned. 7. Meanwhile, degrease the braising liquid in the pot and, if necessary, boil it down until it just turns syrupy. Season to taste with salt and pepper. To serve, remove hand discard the twine, cut chunks of meat from the shanks, transfer to plates, and ladle on some of the sauce. Pass the extra sauce at the table.