Melt the butter and brown sugar together in a medium saucepan over medium heat, stirring often.
Once melted, bring to a full boil, then cook for 1 minute or until the mixture is slightly thick, stirring constantly to avoid burning.
Remove from the stove and let cool for about 5 minutes, stirring often to prevent the bottom from scorching in the residual heat.
Gradually add the milk to the mixture, stirring constantly until the milk is fully incorporated.
Stir in the salt and vanilla.
Transfer the mixture to a heatproof mixing bowl and using a stand or hand mixer, gradually beat in the powdered sugar until you reach a spreading consistency.
This icing gets a little crisp on the surface when it starts to cool. If this happens before you start to frost your cake, just mix it for a few seconds and it will be good to go.