For the pudding, bring 2 cups milk to a boil over medium heat.
While the milk is heating, combine the sugar, cornstarch and salt in a medium bowl.
Whisk in the remaining milk and beat until smooth. Whisk in the egg and beat until smooth.
When the milk is boiling, add a spoonful at a time to the sugar mixture, stirring constantly, until all of the hot milk is slowly incorporated and the mixture is completely smooth.
Return mixture to the saucepan and cook, stirring constantly so no lumps form, for about 2 more minutes or until thickened.
Remove from heat and stir in vanilla.
Place a piece of plastic wrap directly over the surface of the pudding.
Refrigerate until chilled.
When ready to serve, spoon about 2/3 cup of pudding into each cup.