Freeze the raw lobster for 2 hours prior to cooking. Bring a large pan of water to the boil, salt it well (1 tsp salt to every 600ml/1 pint water) and cook the lobster for 15-20 minutes depending on size. When cooked, remove from the water, cut in half lengthways and set aside, reserving the water you cooked it in.
In a separate pan, heat the olive oil and add the tomatoes, onion, tomato puree, red pepper and sea salt, and cook for 10 minutes over a medium heat. Add 500ml of the lobster cooking liquid and the spaghettini. Cook for 10 minutes or until the spaghettini is al dente. Add the basil leaves and lobster to the pan and warm the lobster through for about 3 minutes.
Serve in a large bowl with the spaghettini in the middle and the lobster halves either side.