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 10 minutes.
Add the tomato, garlic, thyme, tarragon, bay leaves, peppercorns, brandy and sherry, stirring, until almost all liquid is evaporated, about an additional 5 to 8 minutes.
Stir in the fish stock and simmer the mixture on medium-low heat, uncovered, stirring occasionally, for about 45 minutes until the mixture has reduced by about half.
While simmering, bring a large pot of water to a gentle boil. Add the lobster tails and poach for about 5 minutes, until just cooked through (do not overcook the lobster or the meat will become rubbery.)
Remove them from the water and set aside to cool. 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, and continue then remove from heat.
Bring a large pot of water to the boil; add the salt and bring back to the boil. Pour in the pasta and cook, stirring occasionally, until al dente, about 10 minutes. Drain and return the pasta to the pot. Ladle in the enough of the sauce to lightly coat the pasta.
To serve, ladle the pasta with sauce into warmed pasta bowls. Serve hot.