Add butter and brown sugar to a medium pot over low heat and stir constantly until sugar melts. Add sugar mixture to scalded milk, slowly, and stir until blended.

In another bowl, stir together cornstarch, salt and cold milk. Add to scalded milk mixture.

Cook on medium heat until thickened, stirring constantly. Cool slightly and then add vanilla. Stir.

Pour pudding into individual serving dishes. Serve warm or cold, topped with nuts or whipped cream.