In a heavy 3-qt. saucepan, combine butter, brown sugar, corn syrup and milk; bring to a boil over medium-high heat. Cook and stir until mixture reaches 248° (firm-ball stage) on a candy thermometer, about 30-40 minutes. Remove from the heat; stir in vanilla. Insert wooden sticks into apples. Dip each apple into hot caramel mixture; turn to coat. Set on waxed paper to cool. If desired, roll the bottom of the dipped apples into chopped peanuts.