

Not an ounce of lobstery goodness goes to waste.
Using the tip of a knife, pierce the heads of the lobsters and cut the bodies in half lengthwise. Remove and discard the stomach. Remove and reserve the roe (if any). Remove the legs, claws, and knuckles from the body and refrigerate.
Gently whisk the heavy cream with any roe (pass it through a strainer first) in a small mixing bowl. (If there’s no roe just omit). Season the flesh side of the lobster bodies with the salt and pepper and then brush with the roe cream (or just plain cream).
Blanch 1 c. of the tarragon in a small pot of boiling salted water for 10 seconds. Shock in a bowl of ice water, remove from the water, and transfer to a blender. Blend on high speed with 1 tbsp. of the ice water to make a puree. Strain through a strainer. Using a rubber spatula, combine the tarragon puree with the butter, smoked paprika, salt, and lemon juice until fully emulsified. Chop the remaining 1 tbsp. tarragon and fold it into the butter.
Bring a large pot of salted water to a boil. Add the lobster knuckles and claws to the boiling water and cook for 4 minutes. Remove from the water. When cool enough to handle, remove the meat from the shells with a pair of scissors.
Heat the butter in a large sauté pan over medium heat until it begins to foam. Add the lobster bodies, flesh side down, and sauté for 2 minutes. Flip the lobsters and cook, basting with the butter, for 1 minute. Add the warm knuckles and claws and some tarragon sprigs to the pan and squeeze fresh lemon juice over the lobsters.