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Place the lobsters in the boiling water headfirst and cover tightly with the lid. (If you happen to have lobsters of different weights, put the heaviest lobster in first, and wait a minute to add the others.) Boil the lobster for about 7 minutes and no longer than 8 minutes. You want it to be slightly underdone. Transfer the lobsters to a bowl and separate the heads from the tails, reserving them both in the bowl. Remove the lobster legs from the body/head and set aside.
Heat the olive oil and lobster heads in a large 14-inch saute pan. Include any juices that have collected in the bowl. Roast the lobster heads in the oil for about 5 minutes.
Meanwhile, crack open the claws and remove the meat. Cut open the tails to remove the tail meat. Cut all of the meat into large, 1- to 2-inch pieces.
Remove the lobster heads from the pan and discard. Add the chiles and garlic to the olive oil and cook for a few minutes until fragrant. Add the wine and cook until reduced by half.
Add the tomatoes, sprinkle with sea salt and black pepper and saute until they just begin breaking down.
Cook the spaghetti in the second pot of boiling water along with 2 tablespoons of salt. Cook the pasta for 2 minutes less than indicated on the package instructions. Reserve 1 cup of pasta water and drain the spaghetti.
Add the lobster meat, reserved lobster legs and pasta to the tomato sauce and toss together for about a minute, adding pasta water as needed. Serve immediately with the spaghetti and torn basil, if using.