In a saucepan bring the milk to a boil and add the 1/4C sugar. While this is heating, mix egg, yolks, cornstarch, 3T sugar. Mix thoroughly.
Once the milk has boiled, remove it from the heat and slowly stream it into the egg-cornstarch-sugar mixture while stirring. You're trying not to cook the eggs. Once it's mixed, put it back in the saucepan and bring it back to a boil while stirring constantly.
When it thickens, around when it gets back to the boil, take it off
the heat and stir in the butter and vanilla. Put into a pyrex dish,
cover the top with cling-wrap that's right on the surface (to avoid
forming a film) and put it in the fridge to chill.