Wash the apples and dry them extremely well. Any moisture or wax on the outside can prevent the caramel from sticking. Insert a food-safe stick firmly into the top of each apple.
Line a baking sheet or plate with parchment paper and lightly grease the parchment.
In a heavy-bottomed saucepan, combine the butter, brown sugar, corn syrup, sweetened condensed milk and salt.
Cook over medium heat, stirring frequently, until the butter has melted and everything is completely combined.
Continue cooking, stirring constantly to prevent scorching, until the caramel reaches 235–240°F on a candy thermometer. For a soft caramel coating, I would begin checking its consistency around 235°F rather than automatically taking it all the way to 240°F.
Remove the saucepan from the heat and carefully stir in the vanilla.
Let the caramel sit for about 5 minutes, or until it has thickened slightly but is still fluid enough for dipping.
Tilt the saucepan and dip each apple into the caramel, rotating it until coated. Allow the excess caramel to drip back into the pan, then place the apple onto your prepared parchment.
Let the caramel apples cool and set completely before putting them on the cake.