Bring 1/2 cup brown sugar, 1/4 cup butter, and 3 Tbsp. milk to a boil in a 2-qt. saucepan over medium heat, whisking constantly; boil 1 minute, whisking constantly. Remove from heat; stir in vanilla. Gradually whisk in powdered sugar until smooth; stir gently 3 to 5 minutes or until mixture begins to cool and thickens slightly. Pour immediately over cooled cake.