In a medium saucepan, pour in 1 cup of apple cider and set it over medium heat. Allow it to simmer gently for 10-15 minutes, stirring occasionally, until reduced to about 1/4 cup. Remove from heat and let cool completely.

In a large mixing bowl, cream together 1/2 cup of softened unsalted butter and 1 cup of brown sugar until light and fluffy. Beat in 1 room-temperature egg and 1 teaspoon of vanilla extract until well blended. Fold in the cooled apple cider reduction until combined.

In a separate bowl, whisk together 1 1/2 cups of all-purpose flour, 1 teaspoon baking powder, 1 teaspoon baking soda, 1 teaspoon ground cinnamon, 1/4 teaspoon ground nutmeg, 1/4 teaspoon ground cloves, and a pinch of salt.

Gradually add the dry ingredients to the wet mixture, alternating with 1/2 cup of whole milk, until everything is incorporated.

Preheat oven to 350°F (175°C) and line two baking sheets with parchment paper. Drop rounded tablespoons of batter onto sheets, spacing 2 inches apart. Bake for 10-12 minutes until the tops spring back when lightly pressed.

While cookies cool, make the buttercream by beating 1/2 cup of softened unsalted butter until creamy. Gradually add 2 cups of powdered sugar and mix until combined. Add 1 tablespoon of cider reduction, 1 teaspoon of vanilla extract, and a pinch of salt, beating until fluffy.

Pair cooled cookies by size, pipe or spread a generous amount of buttercream on one cookie, drizzle caramel sauce, then top with a matching cookie. Chill in the refrigerator for 20 minutes to set the filling.