Melt the butter over medium heat. Add the apples, brown sugar, cinnamon, maple syrup, lemon juice, and salt. Cook 5 minutes or until the apples are tender. Add a cornstarch slurry using cornstarch and apple cider or water. Remove from the heat and let cool.

For the cookies, beat the softened butter, brown sugar, and granulated sugar with a paddle attachment until light and fluffy. Add the egg and vanilla and mix on low until incorporated. Add in the flour, cinnamon, nutmeg, salt, baking soda, and cornstarch. Mix on low until combined.

Scoop about 2 tbsp of dough per cookie onto a baking sheet. Bake at 350 for 10-12 minutes.

While the cookies are still warm, gently press the back of a spoon into the center of each cookie to create an indent. Cool for 15-20 minutes.

For the frosting, beat the cream cheese and butter until fluffy. Add the powdered sugar, vanilla, and salt. Mix on low until combined, then increase the speed and mix until smooth.

Transfer the frosting to a piping bag or a sandwich bag with a corner snipped off. Pipe a ring around the indent of each cooled cookie, then spoon the cooled apple filling into the middle. Finish with a drizzle of caramel.