Melt the butter in a 3–4 quart saucepot over medium heat. Add the onion, garlic, carrot, thyme and bay leaf and cook for 5–10 minutes or until the onion is translucent. Add the lobster tails (shell and everything) to the pot and let them cook for about 2 minutes. The shells will turn pink. Add the white wine and the tomatoes and simmer the lobster tails for 10 minutes. Add the chicken stock and continue to simmer for another 20 minutes.
Remove the lobster tails from the pot and once they are cool enough to handle, crack the shells and remove the meat, keeping the meat in once piece as much as possible. Discard the shells and reserve the meat.
Remove the bay leaf from the pot and then using either a blender, food processor, food mill or immersion blender, puree the soup until no lumps remain and the soup is smooth. Return the soup to the stovetop and add the cream and fresh tarragon. Bring to a simmer and season to taste with salt and freshly ground black pepper.
Garnish with a dollop of créme fraiche or sour cream, dragging a skewer through the dollop to form a heart.
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