In a medium saucepan, whisk together milk, sugar, cornstarch, and salt.
Cook over medium heat, stirring constantly with a wooden spoon or heatproof spatula until mixture thickens and boils.
Boil for 1 minute while stirring.
Remove from heat and stir in butter and vanilla.
Pour into individual dishes or one large dish. Cover with plastic wrap, making sure the plastic wrap touches the surface of the pudding to prevent a skin from forming.