Pour the apple cider into a small saucepan and bring to a gentle simmer over medium heat.
Simmer for approximately 15–20 minutes, or until the cider has reduced from 1 cup to approximately 1/4 cup.
Transfer the reduced cider to a small heat-safe container and allow it to cool completely.
In a medium bowl, whisk together the flour, baking soda, cinnamon, nutmeg, and salt.
In a large mixing bowl, beat the softened butter, brown sugar, and granulated sugar for 2–3 minutes until creamy.
Add the egg and vanilla extract and beat until combined.
Pour in the completely cooled reduced apple cider and mix until incorporated.
Gradually add the dry ingredients and mix just until a soft dough forms.
Cover the dough and refrigerate for 30–45 minutes.
Preheat the oven to 350°F (175°C) and line two baking sheets with parchment paper.
Combine the granulated sugar and cinnamon for the coating in a shallow bowl.
Scoop approximately 1 1/2 tablespoons of dough per cookie and gently roll into balls.
Roll each dough ball generously in the cinnamon-sugar mixture.
Arrange the coated dough balls approximately 2 inches apart on the prepared baking sheets.
Bake for 10–12 minutes, until the edges are set but the centers still appear slightly soft.
Allow the cookies to cool on the baking sheet for 5 minutes.
Transfer to a wire rack and cool before serving.