In a bowl, whisk together sugar, egg and vanilla.

In a small saucepan, heat the milk over medium heat until it is steaming. Gradually add a bit to the egg mixture, stir to combine, then add to the saucepan. (By adding a bit to the egg mixture first, it will help prevent getting scrambled eggs).

Stir over low heat, stirrig constantly, for 5 - 8 minutes or until slightly thickened. Do not boil.

Pour the sauce into a bowl. Place a piece of plastic wrap on the surface of the sauce. Chill.