Place the popped popcorn in a large mixing bowl and set it aside.
In a medium saucepan over medium heat, melt the butter. Stir in the brown sugar, apple cider, and corn syrup until the mixture comes to a boil.
Let the caramel boil for 2 minutes without stirring, then remove the pan from the heat.
Quickly stir in the apple pie spice, green gel food coloring, baking soda, and vanilla extract until the mixture is smooth and the color is even.
Pour the hot caramel over the popcorn and stir gently until all the popcorn is coated.
Let the mixture cool for 2 minutes, then add the chopped dried green apples and mix them in.
Lightly grease your hands and shape the mixture into 4 equal balls, pressing firmly so they hold together.
Place the balls on a parchment-lined baking sheet and let them cool completely before serving.