Place chicken broth (or water + 1 teaspoon salt ) in a stock pot over high heat; bring to a rolling boil.
Place lobster tails in stock pot; return to a boil.
Remove tails, set aside to cool; keep stock in the pot.
When lobster tails have cooled, gently cut the back shell of each lobster tail down to the tail fins; lift and separate the shell from the meat; put shells and any liquid from the shells back in stock; return pot to a boil.
Reduce heat to low; cover; simmer 15 minutes; cut cooled lobster meat into bite-sized pieces.
Heat butter and oil in large saucepan over medium heat; sauté onions, carrots, celery, thyme and tarragon (~5 minutes); stir in garlic, black and cayenne pepper; cook ~1 minute more, until fragrant.
Mix in tomato paste, stir and cook for ~1 minute to coat vegetables. Sprinkle flour over all; cook, while stirring occasionally ~2 minutes more.
Add wine, simmer until reduced by half; stir in strained lobster stock, bring to a bubbly boil; reduce heat to low; simmer ~30 minutes, stirring occasionally.
Take off heat, transfer to food processor; purée until smooth; return all to saucepan over medium-low heat; stir in heavy cream and lobster meat; heat through.
