Mix the cornstarch slurry: In a small bowl, whisk 2 tsp cornstarch with 2–3 tbsp of the cold milk until smooth. Set aside.
Warm the milk: In a saucepan, heat the remaining milk, sugar, vanilla sugar (or vanilla extract/paste), and salt over medium heat until hot but not boiling.
Thicken the sauce: Stir in the cornstarch mixture while whisking constantly.
Keep stirring until the sauce gently thickens and coats the spoon — about 1–2 minutes.
(If using egg yolks, see step 4.)
Optional – add egg yolks for creaminess: In a separate bowl, whisk the yolks. Slowly ladle in a bit of the hot vanilla milk while whisking (to temper).
Pour the tempered yolks back into the pot, stirring over very low heat until silky and slightly thicker (don’t boil, or the yolks will curdle).
Finish & serve: Remove from heat. Taste for sweetness and vanilla.
Serve warm, or pour into a jug and chill — it will thicken slightly as it cools.