Combine the brown sugar, salt, butter, and flour in the top of a double boiler. Cook until the butter has melted. Add the milk slowly. Stir and cook until the brown sugar is completely dissolved.
Beat the egg yolks until light, then add a little of the hot milk mixture to the eggs. Slowly add the eggs to the milk and cook, stirring constantly, until thick. Stir in vanilla, then pour into the pie crust.
Refrigerate several hours before serving. Serve with whipped cream.