Melt butter in a 2-quart saucepan; stir in brown sugar and salt. Bring to a boil and boil hard for 2 minutes, stirring constantly. Remove from heat and add milk, stirring vigorously.
Put back over heat and bring to a full boil again. Set aside to cool for about 20 minutes until lukewarm. Stir in powdered sugar and beat until smooth and cool enough to spread.
If frosting stiffens too quickly while spreading, beat in a few drops of milk. Frosts tops and sides of two 8- or 9-inch layers.