- Fill a large stock pot with water and bring to a boil. Plunge lobsters, one at a time, headfirst into boiling water; boil 4 minutes. Remove from water with tongs and transfer to ice bath to stop cooking process; repeat with second lobster.
- Cut off tail and claws; split the tail and remove the meat. Crack the claws and knuckles open to remove the meat; reserve. Rinse lobster bodies and cut body and shells into 2-inch pieces, set aside and reserve.
- Heat butter in large nonstick skillet over medium-high heat as butter begins to foam, add lobster meat pieces, body and shells. Sauté until lobster pieces turn red, approximately 3 minutes; add Cognac and ignite. Add in celery, onion, garlic, bay leaf, thyme, parsley sprigs, chicken broth, and crème fraiche; stir to combine. Bring to simmer over low heat, cover and gently simmer for 15 minutes.
- Meanwhile, bring large saucepan of salted water to a boil. Add pasta and cook according to package instructions, and drain. Reserve.
- Remove lobster meat and cut into 3/4-inch pieces; reserve. Strain lobster shell mixture and reserve lobster broth.
- In the same non-stick skillet, melt butter and add flour. Cook for 2 minutes while stirring constantly. Add reserved lobster broth and continue stirring until sauce thickens. Add cheese and stir until melted. Remove from heat. Season with salt and pepper.
- Add reserved lobster meat and pasta shells. Garnish with fresh chives and serve immediately.
Calories 670, Carbohydrates 47g, Cholesterol 355mg, Fat 32g, Fat Calories 291, Fiber 2g, Protein 45g, Saturated Fat 20g, Sodium 1010mg. Daily Values: Calcium 293.49mg 29%, Phos 447.68mg 45%, Copper 2.84mg 142%, Zinc 7.97mg 53%, Panto 2.95mg 30%, Biotin 0.48mcg 160%, Iodine 0.14mcg 0%, Magnesium 110.14mg 28%, Iron 2.51mg 14%, Vitamin B6 12%, Vitamin C 3%, Vitamin B12 43%, Vitamin D 2%, Vit E-a-Toco 6%, Vitamin A 22%. Percent Daily Values are based on a 2,000 calorie diet.