Heat the milk with vanilla and half of the sugar in a saucepan until steaming but not boiling.

Whisk egg yolks with remaining sugar until pale, then whisk in cornstarch until smooth.

Slowly pour hot milk into the yolk mixture while whisking constantly to temper.

Return mixture to the saucepan and cook over medium heat, whisking nonstop, until thick and bubbling.

Remove from heat and whisk in butter if using.

Transfer to a bowl, press plastic wrap directly on the surface, and chill until cold.