In a pot over medium, heat the milk, 1/4 cup sugar and the vanilla.
Bring to a simmer.
In a bowl, sift the 3T. sugar and cornstarch, Add the eggs to this mixture.
While whisking eggs, pour in some of the simmering milk.
Transfer it all back to the pan and whisk constantly until it's thick like pudding. This will take 5-10 mins on medium low. Keep whisking!
Remove heat and whisk in butter.
Pour into bowl, place plastic wrap directly on the surface and chill.