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1
Coat the outside of the lamb shanks liberally with salt and pepper. Heat the olive oil in a heavy bottomed pot or Dutch oven over medium-high heat. When the oil just begins to smoke, brown the shanks on all sides in batches, about 10 minutes per batch. Remove shanks and set aside.
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2
Pour off all but 1 tablespoon of the remaining oil and drippings. Add the shallots and mushrooms to the pot and cook until just starting to brown, about 5 minutes. Add the garlic, carrots, and tomato paste and cook 5 more minutes, stirring occasionally. Pour in the stout beer and use a spatula to scrape up all of the brown bits in the bottom of the pot.
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3
Return the shanks to the pot and pour in the beef stock. Turn the heat to high and bring the liquid to a simmer. Tie the herb sprigs into a bundle with butcher twine and add them to the pot.
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4
When the liquid comes to a heavy simmer, lower the heat to medium-low and cover. Cook for 21/2 hours, turning the shanks halfway through, or until the meat is almost falling off the bone. Remove the shanks and set aside.
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5
For the root vegetable puree: add the root vegetables to a large pot of lightly salted water and bring to a rolling boil. Cook, uncovered, for about 30 minutes or until the vegetables have softened. Drain the vegetables well and return them to the pot.
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6
Using an electric beater or immersion blender puree the vegetables until smooth. If desired, mix in 2 tablespoons whole milk or unsalted butter to provide a creamier texture. Add salt and pepper to taste and fold in the chives. Set aside until ready to serve.
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7
To finish the lamb: Increase the heat to medium-high and bring the sauce to a boil. Remove the herb bundle and discard. Turn off the heat and add the 2 tablespoons of butter, stirring until melted.
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8
Serve the shanks over the root vegetable puree and top with a spoonful of sauce.
