To cook the lobster:
2-3 fresh lobsters
1/4 cup vinegar
Pot of boiling water
Combine vinegar with boiling pot of water. Put lobsters in another pot and pour boiling water onto live lobsters and let steep for 2-3 minutes. Remove claws and put back in the hot water for another 5 minutes. Lobster meat will be cooked enough to pull meat away from shell. Remove meat from shells. Reserve lobster meat, shells and bodies.
To cook the broth:
Reserved shells and lobster bodies
1/4 cup canola oil
1 1/2 cup chopped tomatoes
1/2 cup chopped carrots
1 bunch tarragon
2 cups heavy cream
Heat oil in large pot. Add lobster shells and sear over medium-high heat for 1-2 minutes (do in batches if necessary). Add tomatoes, carrots and tarragon and cover with water, and bring to boil. Skim off any impurities. Reduce heat and simmer for an hour. Strain stock through a large strainer, smashing the bodies into the strainer to get all the juices. Then strain through a chinois into a clean saucepan.
Return strained stock onto the stove and simmer for a few hours until it has reduced to one cup of liquid. Add the heavy cream and cook until it has reduced to 2 cups.
Serve lobster broth with reserved lobster meat and garnish with chopped chives. Bonne appétit!