Prep: Reduce your apple cider by cooking it, stirring occasionally, in a small saucepan on the stove, over medium-high heat until it reduces down to ½ cup + 2 tbsp. This will take about 35-42 minutes. Let it cool in the fridge so it's room temperature, not hot. Yes, you really do need 5 cups - this produces a very concentrated apple cider flavor, and you won't be able to taste it otherwise. Make the salted caramel sauce by following my recipe here. Stir in the apple cider last. Let it cool to room temperature before using, or make it up to a week ahead and store in the fridge.
Make the Cookie Dough: In a large bowl, cream the softened butter with an electric mixer on medium-high speed. Add the sugars and mix until creamed together with the butter, about 1 minute. Add the vanilla, eggs, and apple cider, and mix until just combined. Add the dry ingredients last, and mix until a dough forms. Chill for 30 minutes to make it easier to roll the dough into balls.
Scoop & Chill the Dough: Scoop the dough into balls about 60-65 grams with a large cookie scoop (about 3-4 tbsp), and place in an airtight container to chill in the fridge for at least 4 hours, or up to 48 hours. You can speed this up by chilling in the freezer for 1 hour, or up to 1 month (see notes below).
Bake the Cookies: Preheat your oven to 350° F. Line a few cookie sheets with parchment paper or silicone baking mats. In a small bowl, stir together the sugar and spices for coating. Roll the dough balls generously in the apple pie spice cinnamon sugar mixture. Place about 6 cookies on each sheet, with room for them to spread. Bake for 11-13 minutes. The edges should look and feel set when tapped with a fingertip, and the centers will be puffy and look just a tad underdone. They will set up as they cool.
Finish the Cookies: Let cookies cool a few minutes on baking sheets, then transfer to a cooling rack to cool completely, or until cool enough to handle. Stir together the apple butter and reduced apple cider in a medium bowl, then brush each cookie with a generous coating and dip in the remaining apple pie spice sugar from earlier (add it to a plate).
Serve + Store: Drizzle cookies with apple cider caramel and dig in! Cookies can be stored in an airtight container in the fridge for about a week. (The caramel needs to be refrigerated.) Let cookies come back to room temp a bit before serving.
Frozen Cookie Dough: Cookie dough balls can be frozen on a lined baking sheet, then transferred to a freezer bag or airtight container once frozen. Bake frozen cookie dough from frozen, adding 1-2 mins to the bake time as needed.