Start by making the apple cider concentrate. Pour the apple cider into a small pan, and bring to a boil. Stir occasionally and let boil until the cider reduces to 1/3 cup, about 20-25 minutes. Let cool for about 10 minutes.
While the apple cider is reducing, start on the cookies. Preheat the oven to 350°F, and line two sheet pans with parchment paper. In a small bowl, whisk together the flour, baking powder, baking soda, salt, apple pie spice, and cinnamon. Set aside.
In a large bowl, whisk together the vegetable oil, dark brown sugar, applesauce, eggs, and vanilla. Whisk in half of the dry mixture followed by half of the apple cider reduction. Repeat with remaining ingredients until the batter is thoroughly mixed. Don't overmix! The batter should be thick and creamy.
Spoon the batter 2 Tablespoons at a time (1 Tbs. for minis) as round as possible at least 2 inches apart. They may be a little runny, but that's ok! Bake, checking for doneness at 8 minutes. To see if they're baked, lightly press the top of a cookie with the pad of your finger. If the cookie springs back, it's done! Be careful not to over bake the cookies, or they will be dry. Place the cookies on a cooling rack and let cool completely.
Salted Caramel Frosting
While the cookies bake, start on your frosting. Place the dark brown sugar and butter in a medium saucepan. Bring to a boil.
Add the heavy cream, and stir to incorporate completely. Let boil for about 3-4 minutes, until the brown sugar is completely dissolved. Remove from heat and stir in the salt and vanilla. Transfer the mixture to a bowl, and let cool for about 20 minutes.
Beat the powdered sugar into the caramel mixture until smooth and fluffy. Add more cream to thin or more powdered sugar to thicken, as desired. Taste, and add more salt as desired.
Using a piping bag, pipe the salted caramel frosting onto the flat side of half of the cookies. Place the other half of the cookies on top of the frosted ones, sandwiching them together. Store in an airtight container at room temperature for up to 3 days, or freeze for up to 2 months.