In a saucepan, whisk together the milk, sugar, cornstarch, and salt until smooth.

Cook over medium heat, stirring constantly until the mixture thickens and starts to boil.

Once boiling, cook for an additional 2 minutes while stirring.

Remove from heat and whisk in the egg yolks, vanilla extract, and butter until well combined.

Pour the pudding into serving bowls and cover with plastic wrap to prevent a skin from forming.

Chill in the refrigerator for at least 2 hours before serving.