In a medium bowl, beat egg yolks well and then gradually stir in milk until well blended.
In a large, heavy saucepan over medium-low heat, mix together sugar, cornstarch, and salt then gradually add in milk mixture, stirring well to prevent lumps.
Continue cooking over medium-low heat, stirring constantly until mixture reaches a low boil (about 20 minutes).
Allow to boil, still stirring constantly for 1 minute. Then immediately remove from heat.
Set pot in a large bowl of ice water, still stirring.
When mixture has cooled a bit, stir in vanilla.
Place a piece of plastic wrap directly on filling to prevent a skin from forming and place in refrigerator until ready to use.