In a large pot of boiling water boil lobster for 6 minutes, remove from the water and shock in ice water to stop the cooking process.
When cooled remove the meat from the tail, claws, and knuckles.
Discard shells and chop the lobster into bite size pieces.
Make sure to have boiling water seasoned with salt and olive oil to cook the pasta.
Drop the pasta in the boiling seasoned water and stir until submerged.
Heat a large sauté pan with 3oz of olive oil.
Add the garlic, shallots, and chilies and sauté until soft about 3 minutes.
Add the white wine and reduce to 1/3.
Add tomato sauce, vegetable broth and ½ of the basil and bring to a boil.
When the pasta is cooked, add the lobster to the sauce and heat through.
Add the pasta and toss to coat the pasta.
Serve in a large bowl and drizzle the remaining olive oil over the pasta and sprinkle the remaining basil.
Click on this link for acceptable methods of killing live crustaceans - RSPCA - Humane killing and processing of crustaceans