In a large heatproof bowl, whisk together the sugar, cornstarch, salt, egg yolks, and egg. Whisk in 1/4 cup of the milk until you have a thick paste. Set aside while you heat the milk. Have ready a fine medium-sized strainer placed over a bowl as you will need to strain the pudding after it''s cooked. Pour the remaining 2 1/2 cups of milk into a heavy bottomed medium sized saucepan and bring just to a boil. Slowly pour the hot milk into the egg mixture, whisking constantly, until the mixture is smooth. Then pour the pudding mixture back into your saucepan and place over medium-low heat. Cook, stirring constantly, until the mixture thickens to the consistency of mayonnaise (about 3-5 minutes). Remove from heat, strain, and whisk in the butter and vanilla extract.
