Bring very large pot of salted water to boil. Add lobsters. Boil until cooked through, about 12 minutes. Reserve the water. When the lobsters are cool enough to handle remove the meat from body and claws, cut into bite size pieces and set aside. Remove tomalley (green matter) and roe from bodies.
Push the tomalley and roe (if using) through a sieve. Melt 4 tbs butter in a large skillet and sauté over low heat for 15 minutes. Add the lobster, shallots or onions, salt and pepper to taste, tarragon and the remaining butter. Sauté for five minutes, then add the sherry or Madeira, fold in the heavy cream and tomato paste. Bring to a boil and cook until the sauce thickens.
Cook the pasta in the lobster waster until just tender but still firm to bite, about 10 minutes stirring occasionally. Drain the pasta and add it to the saucepan, toss over medium heat until sauce fully coats pasta. Season with salt and pepper.