• Preheat the oven to 400℉. Line baking sheets with parchment paper.

PREPARE THE COOKIE DOUGH:

• The first step is reducing the cider into a syrup. Be patient, this will take about 15 minutes or longer. Heat the cider in a nonstick saucepan over medium-high heat until it comes to a boil. Continue to cook until it's syrupy and reduced to about ¼ cup. Set aside to cool slightly. 
• In a medium bowl, whisk the flour, cream of tartar, baking soda, salt and cinnamon until smooth. In a separate bowl, use an electric mixer to beat the butter with the white sugar and the brown sugar on medium-high speed until fluffy and smooth, 2 to 3 minutes. Beat in the reduced cider and eggs (the mixture may look slightly curdled). Stir in the flour mixture and the apples, just until combined.
• In a small bowl, stir together the ½ cup white sugar and the apple pie spice. Roll heaping tablespoons of dough into balls, using lightly moistened hands if the dough is too sticky, and then roll generously in the spiced sugar mixture. Place the dough balls 3-inches apart on the prepared baking sheets. Bake until the edges are just set but centers are still soft, 10 to 12 minutes. Cool 2 to 3 minutes on the baking sheet, and then transfer to a wire rack to cool completely.