In the top pan of a double boiler combine the sugar, salt, and cornstarch. Add the milk gradually, stirring to dissolve the dry ingredients. Cook over simmering water, stirring constantly, until the mixture is heated through.
In a mixing bowl lightly beat the eggs and stir into them, a little at a time, enough of the hot mixture to heat the eggs to about the same temperature. Combine them with the remaining hot mixture. Continue cooking and stirring until the mixture thickens. Remove the pan from over the water and stir in the butter and vanilla.
Cool the pudding slightly, apportion it equally among 6 individual serving dishes, and chill.
Serve with cream, or fruit or berry purée.