Bring water to a boil in a large Dutch oven; add lobster tails. Return to a boil; cook 5 minutes. Remove tails from water with kitchen tongs; rinse under cold water. Drain.
Split lobster tails lengthwise, leaving bottoms of shells attached. Remove meat, and cut into bite-size pieces. Set meat aside. Rinse shells thoroughly, and let dry. Press shells open flat, and place in a 13- x 9- x 2- inch baking dish.
Melt butter in a heavy saucepan over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add whipping cream; cook over medium heat, stirring constantly, until thickened.
Gradually stir 2 tablespoons hot mixture into yolk; add to remaining hot mixture, stirring constantly. Stir in mushrooms, chives, salt, and mustard. Cook over low heat 2 to 3 minutes. Remove from heat; stir in sherry and reserved lobster.
Sprinkle 1 teaspoon cheese in each lobster shell. Spoon lobster mixture evenly into shells. Sprinkle with remaining cheese and paprika. Bake at 375° for 15 minutes or until browned. Serve immediately.