Whisk together sugar, cornstarch and salt in a small bowl and set aside.
Pour the milk into a medium saucepan set over medium heat and allow to heat until bubble form around the edges. Slowly add the sugar mixture into the hot milk, whisking constantly. Make sure that the mixture does not heat to the point of reaching a boil.
Cook the mixture until the pudding thickens and coats that back of metal spoon.
Remove the pudding from the heat and whisk in the vanilla extract and the butter. Whisk until completely combined.
Transfer to an airtight container or a bowl and cover. Chill for at least one hour to overnight before serving.