First, add the apple cider to a small pot on the stove and bring to a boil over medium/high heat. Reduce the heat to medium/low and let simmer for about 25 minutes or until it reduces to 1/4 cup. It will thicken and get sticky. Set aside to cool slightly.
Add the softened butter to a mixing bowl or bowl of a stand mixer with both the brown and white sugar. Beat with an electric for about 45 seconds. Add in the reduced apple cider, egg and vanilla. Beat to combine.
Spoon and level the flour to measure and add to the bowl, then add in the cornstarch, cream of tartar, salt, baking soda and spices. Beat to combine. The dough will be pretty sticky at this point.
Line a baking sheet with parchment paper and use a roughly 2 tablespoon cookie scoop and scoop the dough onto the parchment. Again, they will be sticky right now. Place in the fridge to set for 1 hour.
Toward the end of the hour, preheat the oven to 350 degrees Fahrenheit.
In a small dish, combine the sugar and cinnamon. Once the dough has set, you'll be able to roll into a ball and then roll in the cinnamon sugar- they won't be as sticky anymore!
Place back on the baking sheet but leave enough room for spreading. I usually do only 6 per baking sheet as they will spread quite a bit. Bake for 13-15 minutes or until the edges are golden brown. Once they come out of the oven, use a round cookie cutter to swivel around the edges to create perfect circles.
Set aside to cool completely. In a small dish, whisk together the powdered sugar and maple syrup. Whisk in the milk if needed. Drizzle on top of the cooled cookies and enjoy!