Put approx. 300 ml milk, the chocolate, the vanilla pulp and the vanilla pods in a saucepan and heat everything while stirring until the chocolate has melted.
Mix the rest of the milk, cornstarch and vanilla sugar with the whisk until there are no more lumps. Now fish the scraped vanilla pods out of the pot.
Bring the vanilla chocolate milk to the boil while stirring, stir in the cornstarch mixture, briefly bring to the boil again until the starch has dissolved. Serve hot or cold.