In a large pot on medium-high heat, sauté lobster shells in soybean oil until completely red. Do not burn. Add onions, fennel and celery. Add tomato paste and stir. Deglaze with brandy and sherry. Add fish stock and tarragon. Heat until reduced by half.
While this is reducing, melt butter in a small saucepan and add flour to make a roux, then set aside. When soup has reduced by half, strain into a new pot, bring to a boil and add cream. Reduce heat and simmer; whisk in the roux. Cook on low heat for approximately 30 minutes.
Lightly sauté the lobster claw meat in butter for use as a garnish.
Serving Suggestion: In the center of a bowl, place lobster claw meat on a puff pastry box or crostini and sprinkle with fresh tarragon. Pour soup around this.