Pour the apple cider into a small saucepan and heat to a simmer. Continue to simmer until reduced to about 4-5 tablespoons (this will take about 20 minutes). Remove from heat and set aside to cool in the fridge.
Preheat oven to 350° and line a sheet pan with parchment paper.
Add the brown sugar and softened butter to a large mixing bowl, and using a stand mixer, beat the butter and sugar until well combined (about 1-2 minutes).
Add the egg and 4 or 5 tablespoons of the apple cider (see notes) and mix until well combined.
Add the flour, cinnamon, cream of tartar, and baking soda and mix until well combined.
Scoop the cookie dough into 2-inch balls, then roll in cinnamon sugar mixture and place on a baking sheet. Flatten each cookie ball slightly with your hand. Bake in the preheated oven for 10-12 minutes, or until starting to crackle on the tops.
Allow the cookies to cool, then serve!
Notes
***I tested this recipe with both 4 tbsp and 5 tbsp of the apple cider mixture and both work great. If you accidentally reduce the apple cider down too far, just add back enough water to make it 4 tbsp.