Boil the lobster claws in hot water for 10-15 minutes or until cooked. Remove from shell and cut the lobster claws into small pieces. Peel, slice and remove the seeds from the mangoes. Cut the mangoes into small cubes.
Put the mangoes and lobsters in a bowl. Add in the cream, honey, lemon juice, and chopped sweet basil. Mix well, cover, and chill in the fridge for at least 30 minutes before serving.