Mix the cornstarch, sugar, and salt with 1/4 cup of cold milk.
In a small pot, heat the remaining milk over low heat (Do not boil!).
While whisking, slowly add the cold milk mixture to the heated milk, stirring constantly, in a heavy bottomed pan or a double boiler.
Continue to cook over low heat, whisking constantly, for 15 minutes until the raw taste of the cornstarch disappears and it thickens. (Do not boil!). It will thicken all at once at the end of the cooking time.
Let cool, then add the vanilla.
Cover and chill.
For Chocolate Blancmange, when you heat the milk, add 2 oz. unsweetened chocolate and stir until smooth.