Heat the oil in a large heavy pot over medium-high heat until hot. Sauté the onion, celery, and carrot (a mirepoix) until the onion becomes translucent and soft, about 8 minutes.
Add the tomato, garlic, thyme, tarragon, bay leaves, peppercorns, brandy and sherry, stirring, until almost all liquid is evaporated, about an additional 6 to 8 minutes.
Stir in the fish stock and bring to a simmer over medium-low heat.
Add the lobster tails and cover the pot. Cook for 6 minutes, until just cooked through (do not overcook the lobster or the meat will become rubbery.) Remove the tails set aside to cool on a cutting board.
Continue to simmer the sauce, uncovered, for an additional 30 minutes, until reduced by half.
Once cool, hold the lobster tail in your hand with the underside facing up. Using scissors cut up the underside and pull out the meat. Chop the meat into bite-size pieces and set aside.
Remove the pot from the heat and pour the mixture through a fine sieve into a large saucepan, pressing on the solids to extract as much liquid as possible; discard the leftover solids.
Whisk the tomato paste into the strained broth then whisk in the cream. Simmer for 15 minutes, until the broth is slightly thickened, stirring occasionally. Turn the heat down to low and season with salt and pepper, to taste. Begin to whisk in the butter one cube at a time until it has all been added to the sauce. Add the lobster meat, stirring to combine then remove the sauce from heat.
Bring a large pot of salted water to a boil. Add the pasta and cook, stirring occasionally, until al dente, about 10 minutes. Reserve 1 cup of the pasta cooking water. Drain and return the pasta to the pot.
Add the sauce and ½ cup of the pasta cooking water, tossing to coat. To serve, ladle the pasta with sauce into warmed pasta bowls. Serve hot.