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1
With a sharp knife, cut the loin meat from the bones of each rack, leaving it in one piece and reserving the bones of one of the racks. Remove any excess fat and trim the silverskin from the loins. Rub with the miso and sprinkle with the thyme. Cover and let marinate in the refrigerator for at least 4 hours and up to overnight.
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2
Cut between the bones to separate them. Heat a large saucepan over high heat, add the bones, and cook until well browned on all sides, about 8 minutes. Remove the bones to a plate and drain all but 1 tablespoon of the fat from the pan. Add the onion and garlic and saute over medium-high heat until browned, about 5 minutes. Add the wine and stir to scrape up any browned bits. Simmer until reduced by half, about 5 minutes. Add 1 1/2 cups of the stock, half of the blackberries, and the lamb bones. Bring to a boil, then lower the heat and simmer until thick, about 40 minutes. Pour through a fine-mesh sieve into a small saucepan and cover to keep warm.
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3
Put the remaining 1/2 pint blackberries, the vinegar, and the sugar in a small nonreactive saucepan. Bring to a boil, stirring, then simmer until the sauce is thick and syrupy, about 15 minutes. Pour through a fine-mesh sieve into a small bowl and set aside.
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4
Put the pistachios and the remaining 1/2 cup stock in a small saucepan, season with salt and pepper to taste, and simmer until soft, 8 to 10 minutes. Set aside.
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5
In a small bowl, combine the shallot, olives, and 1 teaspoon of the oil. Set aside.
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6
Preheat the oven to 450u00b0 F. Scrape the miso paste off the lamb loins. In a heavy skillet over high heat, cook the lamb until well browned on all sides, about 6 minutes. Transfer to a roasting pan and roast until the internal temperature registers 120 to 130u00b0 F for rare to medium-rare, about 6 minutes. Remove to a cutting board and let rest for 10 minutes.
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7
While the lamb is resting, in a medium saute pan, heat the remaining 1 teaspoon oil and the butter over medium-high heat. Add the mushrooms, season with salt and pepper to taste, and saute until browned in spots and soft, about 10 minutes.
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8
Divide the mushrooms among 4 serving plates. Arrange the lamb slices on top and spoon some of the lamb sauce over them. Top with a small spoonful of the olive mixture, scatter some pistachios around the plate, and drizzle with the blackberry-vinegar syrup. Serve immediately.
