Add apple cider to a medium saucepan. Bring to a boil over medium-high heat and cook, whisking occasionally, until reduced by two-thirds. Cook until reduce to a little less than ¼ cup. This should take 20-25 minutes. Pour into a heat proof bowl and set aside to cool.

Preheat the oven to 350°F. Line a large baking sheet with parchment paper.

In a large mixing bowl, use a handheld mixer on medium-high speed to cream together the butter, ½ cup granulated sugar, and brown sugar until light and fluffy. Add 2 tbsp of the reduced apple cider, vanilla, cream of tartar, cornstarch, baking soda, and salt. Beat on medium speed until combined. Add the flour and spices. Beat on low until a soft dough forms.

To make the cinnamon sugar, whisk together ¼ cup granulated sugar and 1 tbsp cinnamon. Use a 1.5 tbsp cookie scoop to portion dough. Roll the dough into a ball, coat in cinnamon sugar mixture, then roll again to form an even ball. Place dough balls on prepared baking sheet.

Bake cookies for 11-12 minutes. The cookies will be puffy and soft and will form some cracks once cooled. Cool cookies on the baking sheet for 10 minutes before transferring to a wire cooling rack. While cookies are cooling, prepare the icing. Whisk together powdered sugar, reduced apple cider, and spices until creamy. Top cookies with icing and enjoy!