Give the egg, sugar and vanilla sugar (or pure vanilla extract) to a bowl. If using a vanilla pot, halve it lenghtwise and scrape the seeds out of the pod. Give the seeds to the bowl with the egg and sugar.
Whisk well until frothy.
Add the cornstarch and whisk very well again, making sure that the mixture doesn't have any clumps.
Slowly pour in the milk while whisking.
Transfer the mixture to a saucepan and gently bring to a boil while whisking almost constantly.
Let the vanilla sauce bubble shortly while whiking continously until it thickens slightly.
The vanilla sauce will continue to set while it cools, so don't let it get too thick at this point, the consistency you are aiming for is slightly thicker yet pourable.
Serve hot, warm or cold as suggested above.
The German vanilla sauce can be easily reheated. Heat it gently in a small pan, while stirring continously and adding a small splash of milk to make it slightly thinner again.