1. Split the lobsters in two lengthwise. Remove stomach sacks (in the head) and intestinal tubes. Reserve coral and green matter. Remove claws and joints and crack them. Separate tails from chests. (Watch Jody's Breaking Down a Lobster to see how this is done.)
2. Heat the oil in the skillet until it is very hot but not smoking. Add the lobster pieces, meat-side down, and saute for several minutes, turning them, until the shells are bright red. Remove lobster to a side dish
3. Stir in the diced carrot and onion, and cook slowly for 5 minutes or until almost tender.
4. With the skillet over moderate heat, pour in the cognac. Avert your face while you do this and ignite the cognac and shake the skillet slowly until the flames have subsided. Season the lobster, return it to the skillet, and add the shallots and the garlic. Stir in tomatoes, tomato paste, fish stock or clam juice, wine, parsley, and tarragon. Cover and simmer for 10 minutes, stirring the lobster occasionally during this time
5. While lobster is simmering, make the compound butter.  Force the lobster coral and green matter with the butter through a fine sieve into the mixing bowl and set aside
6. When the lobster is done, remove it to a side dish. Set skillet with its cooking liquids over high heat and boil down rapidly until sauce has reduced and thickened slightly. It will acquire more body later when the butter and coral mixture is added. Taste very carefully for seasoning
7. Beat a couple of spoonfuls of hot pan juices by driblets into the coral and butter mixture. Return the lobster to the sauce, turn off heat, then pour the butter mixture into the skillet with the lobster and stir to coat the lobsters
8. Arrange the lobster on a serving platter. Thin sauce with water if necessary, then pour over lobster arrangement. Decorate with herbs, and serve immediately

Serving Suggestion

• Garnish with fennel, parsley leaves and edible flowers. Serve with pasta or rice with a glass of Chablis.  Bon appetit!

Adapted from Mastering the Art of French Cooking
by Julia Child, Louisette Bertholle, Simone Beck, and Sidonie Coryn