Meanwhile, in 2-quart heavy saucepan, melt 1/4 cup butter over medium heat. Stir in brown sugar with whisk. Heat to boiling, stirring constantly. Stir in milk. Return to boiling. Remove from heat; cool until lukewarm, about 30 minutes. Stir in 1/2 teaspoon vanilla; gradually stir in powdered sugar until spreadable (add additional milk if frosting becomes too thick). Frost cupcakes. Sprinkle with sea salt.