Mix together sugar and cornstarch in a large saucepan. Add egg yolks and whisk to combine; then gradually whisk in milk.

Cook over medium-low heat, stirring constantly, until custard thickens to the consistency of thick cream, about 25 minutes.

If the custard has lumps, strain through a fine mesh strainer.

Transfer to a large bowl, and add vanilla.

Cover surface of custard with plastic wrap to prevent a skim from forming.

Refrigerate until completely chilled, about 2 hours.