Bring almost all the milk to a boil in a saucepan with the broken pieces of chocolate and vanilla pod. Separate the eggs and beat the egg whites until stiff. Stir the egg yolks with the sugar until foamy, then stir in the cornstarch and the remaining milk.
While stirring, gradually add the chocolate milk mixture to the egg yolk mixture. Add back to the pot while stirring and bring to a boil again.
Remove from heat, beat briefly and fold the egg whites into the hot mixture. Remove the vanilla pod. Place chocolate pudding in bowls and let cool before serving.