An amazing way to serve lobster, taking advantage of almost all the parts of a lobster.
Bring a large pot of heavily salted water (1 cup sea salt) to a boil. Add the lobsters. Boil until cooked through, about 12 minutes (they turn bright red when they are done. Using tongs transfer the lobsters to a baking sheet. Remove the tail and claws and remove the meat to a separate bowl. Remove the roe aka coral from the lobster if any is present and place in a small bowl. Discard the tomalley (the green stuff) from the bodies and discard. Reserve all the parts of the lobster other than the tomalley for later use.
Heat oil in a haven large pot over medium head. Add the reserved shells and body parts from the lobsters, and saute for 3 minutes.
Add the tomatoes, wine, vinegar, garlic, tarragon, thyme, and parsley to the sauted shells. Add the cream and boil for 2 minutes. Reduce heat to medium - low. Simmer for 20 minutes, stirring occasionally.
Strain sauce into a large bowel pressing on the solids to extract as much liquid as possible. Discard contents of strainer or better yet transfer it back to the large pot to use for making lobster stock, there is still plenty of flavoring hiding in whats in the strainer.
Transfer the sauce to a large heavy saucepan (cast iron is best). Cut lobster meat into bit size pieces (except the tails and claws) and coarsely crumble the roe. Add lobster meat and roe into the sauce. Gently rewarm over low heat, stirring occasionally.
Melt butter in separate sauce pan, and saute lobster tails and claws for 1 - 2 minutes. Slice the tails, keeping the shape of the tail and leave claws whole. Reserve butter.
Cook pasta according to package directions. Reduce the cook time by 3 minutes. Drain pasta and return to pot. Add sauce; toss over medium high heat for 4 minutes.
Transfer to large shallow bowl or plate, lay the lobster tails over the prepared pasta and garnish with thyme and tarragon springs. Serve claws on the side whole.