In a small saucepan, combine the brown sugar, cornstarch and salt. Add milk and egg yolk; stir until smooth. Cook and stir over medium heat until mixture comes to a boil. Cook and stir until thickened, 1-2 minutes longer.
Remove from the heat; stir in butter and vanilla. Cool to room temperature, stirring several times. Pour into two individual dessert dishes. Cover and refrigerate until chilled, 1-2 hours.