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Choose a stock pot, Dutch oven or braising dish that will hold the shanks and other ingredients so that the shanks can sit in one layer.
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Pat the shanks dry with paper towel. Heat the vegetable oil in the pot over medium heat and brown the shanks on all sides, about 10 minutes. You may need to work in batches. When the shanks are browned, transfer them to a plate or platter and season well with salt and pepper.
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Pour out the used oil from the pot and replace with the olive oil. Cut off just enough of the garlic head to expose the tops of the cloves. Toss the garlic, carrots, onions and rosemary into the pot. Season with salt (about 1 tsp) and cook over low heat, stirring until the vegetables are softened but not coloured, about 10 to 15 minutes.
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Meanwhile open the can of tomatoes and pour everything into a bowl. Using your hands to crush the tomatoes into bite sized chunks. This is one of the best feelings ever in the kitchen!
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Stir the anchovies or Worchestershire sauce into the vegetables in the pot. Cook for about 1 minute. Add 1 cup of the white wine, turn up the heat and boil till the wine has almost evaporated. Add the remaining white wine, the broth, the tomatoes and their juices, the olives and the citrus peel and the pepper into the pot. Stir everything to combine.
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Add the lamb shanks to the pot. Ideally they should fit in one layer, and should be at least 3/4 submerged under the liquids. Bring to a boil, place a lid on the pot, and then reduce the heat to low to keep everything at a gentle simmer. There should be some bubbling going on. Adjust the heat to maintain this.
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Braise as such for 2 hours and then check the shanks, if the meat is falling off the bones, they are ready! If not, keep cooking until this is achieved. Check after every 30 minutes or so.
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Pick out the garlic cloves, and serve the shanks with the sauce. Garnish with fresh rosemary if desired.
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Serve over mashed potatoes, puréed parsnips, rice, couscous or even orzo.