Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a small saucepan, reduce the apple cider over medium heat until it reaches 1/4 cup, about 20-25 minutes. Let it cool.
In a medium bowl, whisk together the flour, baking soda, cinnamon, nutmeg, and salt.
In a large bowl, use an electric mixer to cream the butter and sugars until light and fluffy, about 2-3 minutes.
Beat in the egg until well combined.
Gradually mix in the flour mixture until just combined, being careful not to overmix.
Stir in the reduced apple cider.
Chill the dough for at least 30 minutes to prevent spreading.
Scoop the dough into balls, about 1.5 tablespoons each. Roll each ball in the cinnamon sugar to coat.
Place the balls onto the prepared baking sheet, leaving about 2 inches of space between each cookie.
Bake for 10-12 minutes, or until the edges are set and lightly golden. The centers should look soft and underdone.
Remove from the oven and let cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.