Bring the milk and vanilla sugar to a boil, remove from the heat, and let infuse for 20 minutes. Melt the chocolate with 3 tablespoons of the hot milk. Beat the egg yolks with the sugar until fluffy, and then add the melted chocolate, cornstarch, and milk mixture. Bring to a boil, then remove from the heat.
Beat the egg whites until stiff, and then fold into the hot custard. Whip the cream, and then add to the custard. Transfer the pudding to a dessert bowl and chill in the refrigerator. Garnish with chocolate pieces, and serve with spoons.