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Instructions for simmering liquid
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Combine all the ingredients, except the lobster, in a large pot and bring to a boil over high heat. Reduce heat to medium-low and simmer for 30 minutes. Drain the liquid through a fine-mesh sieve and discard the solids. Return the liquid to the pot and bring it to a simmer again. Prepare a large bowl of ice water and set aside. Place the lobster in the simmering liquid and cook until they turn pink, about 5 minutes. Strain the lobster in a colander and discard the cooking liquid. Place in the ice water bath for 3 to 5 minutes to chill, adding more ice if necessary to cool.
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When the lobster tails are cool enough to handle, use the point of a paring knife to score the underside of each tail and cut a line lengthwise along the middle of each tail. Crack the tails open and pull out the meat. Chop it into small chunks about 1/4 to 1/2-inch in diameter and set aside.
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Instructions for pasta
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In a large pot, bring 4 quarts of lightly salted water to a boil over high heat. Add the pasta and stir it a bit as it softens. Reduce heat slightly, but keep it high enough to maintain a boil without splattering the stove. Cook until the noodles are tender but still firm, 8 to 9 minutes. Drain in a colander and shake dry. (Do not rinse.) Leave the noodles in the colander and set aside.
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Instructions for sauce
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While the pasta is cooking, melt the butter over medium heat in a large saute pan or deep-sided skillet. Add the shallots and saute for 1 minute. Add the garlic and red pepper flakes and cook until fragrant, about 30 seconds. Add the lobster broth, wine, saffron and 1/4 teaspoon salt. Raise heat to high and bring to a boil. Lower to medium-high and let simmer until the liquid has reduced by half, 8 to 10 minutes. Add the cream and continue to simmer, stirring occasionally, until the sauce thickens, about 4 minutes. Add the lobster chunks and cook for another 2 minutes. Remove from heat and serve immediately.
