Place the tartlet shells on a baking sheet and set aside.
Melt the butter in a saucepan over medium heat. Add the brown sugar and stir until the mixture bubbles and turns smooth.
Slowly pour in the heavy cream while stirring. Continue cooking for 3 minutes until the caramel thickens slightly.
Remove the pan from the heat and stir in the vanilla, salt, and green food coloring until the color is even.
Add the apple slices to the warm caramel and stir gently so each slice is coated.
Spoon the apple and caramel mixture into the tartlet shells, dividing it evenly among the four shells.
Let the tartlets cool at room temperature for 20 minutes so the caramel can set before serving.