Wash the apples, and cut them into quarters, pare and core them. Into a saucepan put the sugar and water, and heat. When the sirup boils, add the apples. Cover and boil gently until the apples are tender. Remove the apples from the sirup with a skimmer or a wire egg beater, placing the fruit in sherbet glasses or other suitable dishes for serving.
In another pan, mix the milk and corn-starch thoroughly. Stir and cook until the mixture reaches the boiling point, then add it to the sirup in which the apples were cooked. Boil for a few minutes. Add the salt, butter, and vanilla. Stir these into the mixture, then pour the sauce over the apples. Serve Butterscotch Apples hot or cold for a dessert.