How to Make It
Cook pasta according to package directions. Drain and set aside.
While pasta cooks, bring 8 cups water to a boil in a large stockpot over high. Add lobster, and cook 6 minutes. Transfer lobster to a bowl filled with ice and water; let stand until cool enough to handle. Reserve 1/2 cup of the cooking water. Using scissors or a chef’s knife, remove and discard the lobster shell. Chop meat into 1-inch pieces, and set aside.
Melt butter in a large skillet over medium-high. Add the pasta, cheese, pepper, salt, and 1/4 cup of the reserved cooking water. Cook, stirring constantly, until cheese is melted. If you prefer a creamier sauce, add the remaining 1/4 cup reserved cooking water. Stir in the lobster.
Divide pasta mixture evenly between 2 plates. Sprinkle evenly with tarragon, and serve hot.