2. Cook the live lobsters, in batches, for five minutes each. Do not try to cook all the lobsters at once; they should be cooked in batches to keep the water boiling.
3. After five minutes, remove the cooked lobsters from the pot, place them in the ice water bath and run cold water over them to cool them as quickly as possible.
After cooking the lobsters:
1. Clean and remove all lobster meat from the tail, claws and knuckles. Cut the meat into large pieces and keep cold.
2. Place the lobster shells, carrot, onion, celery, carrot and bay leaf in a large pot. Add enough cold water to barely cover the shells. Place over medium heat and simmer until about one-quarter of the liquid remains. Strain, reserving the liquid.
3. Into another pot, pour just enough extra-virgin olive oil to cover the bottom of the pan.
4. Place over low heat and add the chopped Fresno chili. (If you like spicy foods, add the chili's seeds.)
5. Add the whole garlic clove and cook on low heat with the pepper. Remove the garlic as it begins to color, after about two to three minutes.
6. With the pot still on low heat, add the tomato sauce.
7. Add the strained lobster stock to the pot with the tomato sauce. Cook for one hour over low heat.
8. Cook the pasta in salted water for the time indicated on the box, minus two minutes. (The pasta will finish cooking in the sauce.)
9. Taste the sauce, and add salt to taste.
10. Add the lobster meat and torn basil leaves to the sauce.
11. Strain the pasta, and add it to the tomato sauce, cooking for an additional two minutes to finish the pasta and allow it to absorb flavor from the sauce.
12. Taste again and, if necessary, add salt.
13. Divide into four to six portions and serve.