In a saucepan, whisk together the sugar, cornstarch and salt until combined. Add about half the milk and whisk until smooth. Whisk in the eggs, then the remaining milk. Heat the pan while stirring over medium high heat to a full boil. Drop the heat to medium and whisk for 1 minute (it will thicken rather quickly!) Off the heat, add the vanilla and whisk in the butter a couple lumps at a time until smooth, then chill saucepan in the ice bath you had ready.