Twist off the lobster legs and reserve. Remove and discard the lobster heads; remove the intestinal veins from the tails. Remove the meat from the tails and cut into bite-size pieces. Rinse and dry the shells.
Preheat the griller. Heat the mornay sauce gently in a heavy saucepan and fold the lobster meat through. Spoon the mixture into the lobster shells. Sprinkle with the Parmesan cheese and grill for 2–3 minutes, or until the cheese is melted and lightly browned. Serve immediately, garnished with lobster legs.