Add apple cider to a medium saucepan. Place on the stove over medium heat. Bring to a rolling boil. Allow cider to reduce for about 20 to 23 minutes, stirring occasionally, until there’s only ¼ cup remaining and it has a syrup-like consistency. Cider will thicken more as it cools. Set aside to cool completely.
Add flour, baking soda, cinnamon, ginger, nutmeg, and salt to a medium sized mixing bowl. Whisk to combine.
Add butter and brown sugar to the bowl of your stand mixer, fitted with a paddle attachment. Cream butter and sugar together for about 1 minute, until light and fluffy.
Add in the egg. Beat until smooth. Add in the ¼ cup of room temperature reduced apple cider. Beat again until smooth, scraping down the sides of the bowl as needed.
Pour flour mixture into the bowl with the butter mixture. Beat until just combined and there is no dry flour remaining. Do not overmix.
Place bowl in the refrigerator and chill the dough for at least 10 to 15 minutes.
Preheat oven to 375 degrees F. Prepare 2 baking sheets by lining them with parchment paper.
Scoop out 1 ½ to 2 tablespoons of dough and roll it into a ball. Place on a prepared baking sheet. Lightly flatten the top of the dough with your hand. Continue with the rest of the dough, leaving about 2 inches of space between each one.
Bake cookies for 7 to 9 minutes, or until the tops start to crack and turn lightly golden brown. The middle might look under-baked, but this is okay. It will cook more on the cookie sheet before it cools.
Prepare the apple cider glaze by whisking together confectioner’s sugar, apple cider, and maple syrup in a small bowl until there are no more lumps.
Drizzle glaze over the tops of the cookies. Allow to set for a few minutes before serving.