In a large heavy saucepan, melt butter; add the brown sugar, corn syrup and salt. Cook and stir over medium heat until mixture comes to a boil, about 10-12 minutes. Stir in milk. Cook and stir until a candy thermometer reads 248° (firm-ball stage). Remove from the heat; stir in vanilla.
Insert Popsicle sticks into apples. Dip each apple into hot caramel mixture; turn to coat. Set on greased waxed paper to cool.