Heat milk in a medium saucepan over medium heat until bubbles form at the edges.
Mix sugar, cornstarch, and salt together in a small bowl.
Add sugar, cornstarch, and salt mixture to hot milk, a little at a time, stirring until thick enough to coat the back of the spoon.
Remove saucepan from heat, and stir in vanilla and butter.
Spoon pudding evenly into 5 serving dishes. For best results, chill pudding in the refrigerator before serving.
