Bring a large pot of water to boil. Add 1 tsp salt.
Make vertical cuts in the bottom parts of the lobster tails.
Place the tails into the boiling water and leave for 2 minutes.
Transfer to a large cutting board and let cool.
Carefully pull the shells apart at the place of the cut. Remove the lobster meat watching out for the spikes. Reserve the shells.
Clean the meat from the veins and impurities. Cut into bite sized chunks. (see notes)
Heat a medium pot to medium. Add the shells and fry for a minute. Add 750ml water, bring to boil and simmer for 30-40 minutes. Discard the shells. (see notes)
In the meantime, prepare the tomatoes. Cut them in halves and pour over boiling water. Take out after a minute and let cool. Rub the cut side against a grater over a bowl. The pulp will fall through leaving the skin behind.
Heat 2 tbsp olive oil in a pan. Add the shallots and garlic and fry for a minute until fragrant.
Pour in the wine. Simmer over medium-high heat until the liquid has reduced to 1/4.
Add the pureed tomatoes, chili flakes, 2 tsp tomato paste and 2 ladles of lobster stock. Stir and simmer for at least 10 minutes.
Taste and adjust for salt.
Use hand blender to blitz the sauce until smooth. Reserve 1/2 cups of the sauce. (see notes)
Return the sauce to the pan, add cherry tomatoes and simmer for 5 minutes (this step is optional).
Add the lobster meat to the pan with the sauce. Cook for 2 minutes, checking a couple of times. The lobster is ready when it has turned opaque throughout.
Cook spaghetti one minute short of al dente. Reserve 1/2 cups of cooking water and drain.
Return the spaghetti to the cooking pot and add the reserved tomato sauce (without the lobster) along with 1/2 of reserved pasta water. Cook over medium heat, stirring constantly, for 30 seconds.
Add the sauce with the lobster chunks in it and heat through for about 15 seconds.
Taste the pasta. If dry or not al dente, add the remaining cooking water.
Serve immediately garnished with fresh basil leaves.