Begin by combining 3 tbsp of the milk, egg yolks, and cornstarch in a separate bowl. Whisk to form a paste.
In a medium saucepan, combine the remaining milk, sugar, and salt over medium heat. Stir constantly until the sugar is dissolved and the milk is simmering. Do not scorch your milk.
Remove the milk mixture from the heat, and sit it aside.
Add a ladle full of the hot milk to the egg yolks. Whisk vigorously to temper the yolks.
Once the egg yolks are tempered add them to the milk mixture in the pot. Return to the stove and heat over medium heat whisking continuously. You want to continue to whisk vigorously to prevent lumps from forming in the pudding.
Heat the pudding until it is thickened and slightly simmering.
Remove the pudding from the heat. Stir in the softened butter and pure vanilla extract.
Transfer the pudding to a glass bowl, and cover the top with parchment paper or plastic wrap to prevent a film.
Cool the pudding in the refrigerator for 2 hours prior to serving.
