Prep the apple cider: Pour 1 ½ cups of apple cider into a small saucepan and bring it to a boil on the stovetop over medium-high heat. Boil for 10-15 minutes, or until the cider is thickened slightly and reduced to about five tablespoons. Cool and use as instructed.
Make the cookie dough: Cream butter, sugars, egg, vanilla, and apple cider for 2-3 minutes. In a separate bowl, mix the dry ingredients (flour, baking powder, salt, and spices). Add the dry ingredients to the butter mixture and mix until a soft dough forms.
Roll in sugar coating: Combine sugar, cinnamon, and nutmeg in a small bowl. Use a cookie scoop to scoop the dough into 2-tablespoon-sized balls and then roll the dough balls in the mixture. Place 2" apart on a cookie sheet that has been lined with parchment paper or a silicone baking mat.
Bake: Bake at 375°F for 9 minutes until the cookies are golden brown on the bottoms, but still soft in the centers. Cool for several minutes before transferring to a wire rack to cool completely.
Make the frosting: Beat butter, cream cheese, powdered sugar, cinnamon, and apple cider until creamy and fluffy.
Assemble: Pipe or spread frosting on the bottoms of half the cookies, then sandwich with the remaining cookies.