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In a large bowl, mix 3 cups of water and 1/3 cup lemon juice.
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Cut off the stem of each artichoke approximately 1/2 to 1 inch from the base. Peel the stem. After removing and discarding the bottom and outer leaves, trim 2 inches from the top of the artichoke.
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Cut the artichoke vertically into two pieces, and remove the thistle from the base. Any remaining leaves or dark green layer can be trimmed from the base of the artichoke halves. After rubbing the artichoke edges with a lemon half, place the artichokes halves into the large bowl that contains the lemon water.
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On the stovetop, heat a Dutch oven over medium-high heat. Place the veal into the oven and brown on all sides, including the edges. Add the onions to the Dutch oven, and simmer until tender (approximately 5 minutes).
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Pour one can of broth and the wine into the Dutch oven. When the liquid begins to boil, cover and reduce the heat. Allow the ingredients to simmer for 45 minutes.
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While the veal cooks, remove the artichoke halves from the lemon water and transfer to a skillet. Add 1 cup water, 1/3 cup lemon juice, 1/2 cup dill, one can of broth, salt, and pepper to the skillet. Cover the pan and place over low heat. Allow the ingredients to simmer until the artichokes become soft (approximately 30 minutes).
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Once the veal and artichoke halves have finished cooking, remove with a slotted spoon and transfer to a serving dish to keep warm. Reserve the lemon juices in the skillet.
