In a medium bowl, whisk the egg yolks with the sugar and cornstarch. In a small saucepan, heat the milk. Gradually add the milk to the egg yolk mixture in a thin stream, whisking constantly, until the mixture is smooth.
Return the mixture to the saucepan and cook over moderate heat, stirring constantly with a wooden spoon, until the sauce is thick enough to coat the back of the spoon, about 6 minutes. Stir in the vanilla, transfer the crème anglaise to a serving bowl and serve.
The crème anglaise can be refrigerated for up to 3 days.