Summarize the following:
Wash the shanks and use a sharp knife to remove some of the larger deposits of fat, but don't trim the shanks of all visible fat. The fat will render and contribute to the flavor of the final dish. Pour the oil into a large dutch oven or another oven-safe dish and place it over medium high heat. Allow it to heat completely, until it begins to smoke just slightly. Season the shanks with salt and pepper on all sides. Place them in the hot oil and brown them on all three sides. Brown each side for about 4 minutes, enough to get a good sear on each side. Don't cook the lamb shanks all the way through. Browning them will bring out the deep flavor of the shanks, but longer cooking will bring about the soft, fall-apart texture you want. Make sure the oil is nice and hot before you put the shanks in the pot. Arrange the vegetables and garlic cloves around the lamb shanks, and drop in the peppercorns. Pour the wine over the entire contents of the pot. Let the red wine come to a boil, and boil it for three minutes. Add the water and reduce the heat to bring everything to a quick simmer. Boiling the wine for three minutes will lower the alcohol content a bit, leaving the deep flavor of the wine behind. With the addition of the water, the shanks and vegetables should be fully submerged in liquid. If they aren't, add a little more water. If you don't have a tight-fitting lid for the dutch oven, cover it tightly with aluminum foil. Place it in the oven and braise it for 1 hour and 30 minutes. Every half hour, remove it from the oven and turn the shanks so they cook evenly. After 1 hour and 30 minutes, the shanks should be quite tender. If they aren't, return them to the oven and continue braising, checking every 15 minutes until they've reached the correct texture. Transfer the cooked lamb shanks to a serving platter. Pour the braising liquid through a fine-mesh sieve to strain out the vegetables and keep the liquid. Pour the liquid into a saucepan and cook it over medium heat, stirring often, until it has reduced and become a thick sauce. Season it with salt and pepper to taste. To make the sauce thicker, add a teaspoon of cornstarch. Pour the braising liquid over the lamb shanks and serve the dish with roasted vegetables or mashed potatoes. Each shank is enough for one serving.
Preheat the oven to 325F (163C). Wash and trim the shanks. Heat the oil. Brown the lamb shanks. Add the vegetables, peppercorns and wine. Cover the dish and transfer it to the oven for braising. Strain and reduce the braising liquid. Serve the lamb shanks.