In a small bowl, mix together ¼ cup of the milk with the cornstarch.
In a medium saucepan, whisk together the remaining milk, salt, and sugar. Allow the mixture to heat over medium heat until it is steaming; do not let it boil.
While the milk is heating, whisk the egg yolks in a separate small bowl.
Once the milk is steaming, slowly pour ½ cup of the warm milk mixture into the egg yolks, whisking constantly.
Remove from the heat and stir in the butter and vanilla extract.
Pour into individual serving dishes. Top each with a layer of plastic wrap touching the top of the pudding to prevent a skin from forming. Refrigerate until chilled.