In a small bowl whisk together the sugar, cornstarch and salt. Set aside.
In a medium saucepan, heat cold milk over medium heat, until small bubbles form along the sides.
Whisk in the dry ingredients (the mixture of sugar, cornstarch, and salt). Stir while it's cooking, and allow it to thicken up enough to coat the back of a wooden spoon.
When the pudding has thickened up, remove the pan from the heat and immediately stir in the vanilla extract and butter until well combined.
Chill in the refrigerator for at least 15 minutes before serving.
Notes
Makes approximately 6 servings.Storage: store vanilla pudding in an airtight container in the refrigerator for up to 3-5 days.