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1
Bring a pot of water to a boil and add salt until it tastes like seawater.
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2
Set the lobster tails aside and cook the claws in the salted water for 5 minutes.
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3
Remove and crack open using the back of a knife.
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4
Reserve any interior water and juices from the shells and add it to the final sauce for flavor boost.
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5
Bring another pot of abundantly salted water to a boil, add the spaghetti, and cook until al dente, about 8 minutes.
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6
Drain but do not rinse, reserving 1 cup cooking water.
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7
Cut each tail in half lengthwise and then widthwise, yielding 4 pieces.
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8
Heat 3 tablespoons of the oil in large saute pan over medium heat and add the tail pieces (the shell still attached to the meat).
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9
When the lobster meat begins to look white (about 2 minutes), add the garlic and chiles and cook until softened, 3 to 5 minutes.
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10
Add the reserved pasta water, tomato sauce, and cooked lobster claws and simmer, reducing the sauce to thicken, about 5 minutes.
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11
Add the pasta to the sauce, tossing to coat.
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12
Add the remaining 1 tablespoon oil and any reserved liquid from the claws; season with salt and pepper to taste.
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13
Divide the pasta among 4 warmed serving bowls and sprinkle with mint.
