Bring a large pot of water to a boil over medium heat and season the water with salt.
Cut the lobster tails lengthwise, remove the meat from the shells and chop into 1-inch pieces. Pit and chop kalamata olives and rinse the capers. Set aside.
Heat a large saute pan over medium-low heat. Add the olive oil and heat through. Add the shallots and cook until soft, about 3 to 4 minutes. Stir in the garlic and red pepper flakes and saute for an additional 30 seconds; do not brown the garlic. Add the tomatoes, wine, chicken stock, basil and parsley. Simmer for 15 to 20 minutes.
Add the capellini to the boiling water.
Stir the chopped lobster meat, capers, kalamata olives, butter, and pepper, to taste, to the tomato mixture. Cover the pan and simmer the sauce until the lobster meat is cooked, about 5 to 7 minutes. When the pasta is cooked, drain and add to a serving bowl. Pour the sauce over the pasta and toss. Sprinkle with grated Parmigiano-Reggiano and the chopped parsley and serve.
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