Preheat oven to 375°F (190°C). Line two baking sheets with parchment paper.
In a medium bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In a large bowl, cream butter, granulated sugar, and brown sugar until light and fluffy.
Mix in egg until combined. Add reduced apple cider and blend until smooth.
Slowly add dry ingredients to wet mixture and stir until just combined.
Fold in diced apple with a spatula.
Scoop dough into 1 ½-inch balls and place 2 inches apart on baking sheets.
Bake 10–12 minutes until edges are set and centers are soft.
Cool on baking sheet for 5 minutes, then transfer to wire rack.
Whisk icing ingredients and drizzle over cooled cookies.
