In a medium saucepan, whisk together the milk, sugar, egg yolks, and cornstarch.
Place the pan over medium heat and whisk constantly. This is one of those moments where staying nearby really helps don’t walk away, because it thickens quickly.
As it heats, the mixture will go from thin to thick and creamy. Once it starts bubbling and has a pudding-like consistency, remove it from the heat.
Stir in the vanilla sugar and butter until smooth and glossy.
To prevent a skin from forming, press a piece of plastic wrap directly onto the surface of the pudding. Let it cool completely before assembling.
Little shortcut option: If you’re in a rush, you can use store-bought pudding. But if you have the time, homemade really does make it feel extra special.