Add the butter and brown sugar to a medium pot set over medium heat. When the butter has melted, add the cider and whisk to combine. Bring the mixture to a boil and cook, whisking constantly, until the sugar has melted and the mixture is dark, bubbling, and thickened, about 10 +/- minutes [2]. Stir in the salt. Carefully pour the caramel from the pan onto a parchment-lined baking sheet, spreading the caramel with a heat-proof rubber spatula to an even 1/8-inch thickness. Let it set until cool, then score the caramel with a sharp knife into roughly ½-by-½-inch squares [3].

Arrange the apples on a parchment-lined baking sheet. Bake for 10 minutes to dry the apples out. Remove from the oven to cool, then cut or dice into roughly ½-by-½-inch squares.

Scoop the dough into rounded tablespoon-size balls (squishing the dough together lightly and rolling in the palm of your hands) and place 2 inches apart on the prepared baking sheet. Bake for 8 minutes. Rotate the baking sheet. Bake another 2-3 minutes or until the cookies begin to brown around the edges.

Let the cookies cool on the baking sheet, pushing any melted caramel back to the edges of the cookies with a rubber spatula. Continue to cool until they can be easily moved to a wire rack to cool further.

As the cookies cool, if desired, make the glaze. Whisk together the powdered sugar, maple syrup, vanilla, and a pinch of salt. Thin with more maple syrup if needed. Drizzle or smear the glaze over the top of the cookies! Store in an airtight container for up to 4 days.