In a bowl, whisk together ΒΌ cup of the milk with the cornstarch and set aside.
In a second separate bowl, slightly beat the egg yolks and then set aside.
In saucepan, mix the sugar and salt. Gradually stir in the rest of the milk while cooking over medium heat.
Stir or whisk continuously until the mixture begins to boil and thicken. Over medium heat this should take about 10 minutes.
Let boil for 1 minute.
Turn off the heat. Whisk in half of the hot mixture into the egg yolks. Stir the eggs yolks mixture back into the saucepan and the rest of the mixture.
Optionally, you can use a metal strainer with fine holes to help filter out any egg whites as you are returning the mixture back to the saucepan.
Add the cornstarch mixture to the saucepan.
Restart the heat and boil for another minute. Make sure to whisk continuously. The pudding will thicken up quite a bit during this stage.
Remove from the heat.
Add the butter and vanilla. Whisk well to incorporate.
Pour into pudding dishes or whatever vessel you desire. The pudding will still be very hot, so make sure the containers are heat resent. Tempered glass works very well.
Cover and refrigerate for at least an hour to allow it to chill and set.