(Courtesy of God):
Heat 1/4 cup canola oil in a deep braising pan. Add the lobster shells (he uses three, but you can use two, and that will work fine as well) and sear over medium high for 1-2 minutes per side until red. Add 1 1/2 cup chopped tomatoes, 1/2 cup carrots and a bunch of tarragon and cover the shells with water. Bring to a boil and skim off any impurities that rise to the top. Reduce heat to low and simmer for 1 hour. Strain the stock, crushing the lobster bodies to extract all the juices, and then strain through a fine chinois into a clean saucepan. Reduce until 1 cup remains. Add 2 cups of heavy cream, return to a simmer, and reduce until 2 cups remain. Strain again and chill over ice. Refrigerate for up to 3 days.
To reheat, place the cold broth in a saucepan and whisk vigorously over medium heat.
Serve in an elegant tea cup.