• Plunge lobster headfirst into pot of boiling water, boil 4 minutes. Using tongs, transfer to cutting board. Cut off tail and claws. Crack tail and claws and remove meat. Cut meat into 1/2 inch pieces. Cut body and shells into 2 inch pieces. Chill meat; reserve shells
• Heat 1 tablespoon olive oil in heavy large skillet over medium-high heat. Add lobster body, lobster shells, and shrimp shells to skillet and saute for 4 minutes. Add onion and next 4 ingredients; saute 6 minutes. Add tomato paste; stir 1 minute. Remove from heat; stir in Cognac. Add 3 cups water; bring to boil. Reduce heat, cover, and simmer for 30 minutes.
• Strain mixture into bowl, pressing on solids to extract liquid; discard solids. Set stock aside. Heat 1 tablespoon oil in same skillet over medium-high heat. Add shrimp; saute until just opaque in center; about 3 minutes. Cool slightly. Coarsely chop shrimp.
• Melt 2 tablespoons butter in large saucepan over medium heat. Add flour; stir 1 minute. Add stock and cream; simmer until sauce is reduced to 2 cups, about 5 minutes. Add cheese; stir uuntil smooth. Season with salt and pepper. Remove from heat.
• Meanwhile, cook pasta in large pot of boiling salted water until al dente. Drain. Stir lobster, shrimp, pasta, crab and 2 tablespoons butter into sauce. Stir over medium-low heat until heated through, about 2 minutes. Season with salt and pepper. Serve topped with chives.
