How to Make It
To prepare the lobsters, plunge a heavy chef's knife through each head just above the eyes, making sure the knife goes all the way through the head. Pull the knife in a downward motion between the eyes. Twist off claws where they join the bodies; set claws aside. Twist off tails from the bodies. Reserve bodies. Place tails on a cutting board; press to flatten. Cut in half lengthwise. Remove the vein that runs down the center of each tail. Cover and refrigerate tails.
Bring a large saucepan of water to a boil. Add claws to boiling water; cook 5 minutes. Remove claws from pan, and cool. Separate knuckles from claws. Remove meat from knuckles and claws.
To prepare sauce, heat canola oil in a large, shallow saucepan over medium-high heat. Add lobster bodies to pan; cook for 5 minutes, stirring occasionally. Add shallots and garlic; sauté 1 minute. Add peppercorns and tomato paste; reduce heat to medium, and cook 1 minute, stirring constantly. Stir in brandy and vermouth; cook until liquid is reduced by half (about 5 minutes). Add 2 cups Shrimp Stock; bring to a boil. Reduce heat to low, and simmer 10 minutes. Add cream, basil, and tarragon; simmer for 5 minutes. Strain mixture through a fine sieve over a bowl. Discard solids. Stir in 1/4 teaspoon salt and ground white pepper. Keep warm.
Preheat oven to 350°.
To prepare beurre monté, bring 2 tablespoons water to a simmer in a small saucepan. Add butter, 1 tablespoon at a time, stirring constantly with a whisk until butter melts.
Sprinkle remaining 1/4 teaspoon salt over tails. Brush 3 tablespoons beurre monté over tails. Arrange tails in a baking dish. Bake at 350° for 10 minutes or until done. Add claw and knuckle meat to remaining beurre monté; cook over low heat until thoroughly heated.
Remove tail meat from shells; place one piece of tail meat in each of 4 shallow bowls. Divide knuckle and claw meat evenly among servings, and discard remaining beurre monté. Spoon 1/2 cup sauce over each serving.