1. In a medium pan, warm milk and sugar over medium heat (do not boil), stirring until sugar dissolves. In a small bowl, whisk together cream, egg and cornstarch. Slowly whisk cream mixture into warm milk, whisking constantly.
2. Cook, whisking constantly, until mixture is thick enough to coat back of a spoon, 4 to 6 minutes. Remove from heat; stir in vanilla and butter. Transfer to a bowl and cover with plastic wrap, pressing plastic directly onto surface of pudding. Refrigerate until cold, 1 1/2 hours; pudding will thicken as it cools.
3. Divide half of pudding among 4 parfait glasses. Sprinkle with half of cookies. Repeat layering with remaining pudding and cookies.