Preheat the oven to 375°F. Line two cookie sheets with parchment paper or grease lightly.

In a medium bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, and salt. Set aside.

In a second mixing bowl, cream together butter and sugars with an electric mixer until light and fluffy, about 2 to 3 minutes.

Add the egg and mix just until combined. Add the apple cider and combine. Scrape the sides and bottom of the bowl as needed.

Add the flour mixture and mix at low to medium speed until evenly moistened. Stir in the chopped apple.

Using a 1-inch cookie scoop or tablespoon, scoop the cookies into 1 ½-inch balls. Place onto prepared cookie sheets about 2 inches apart.

Bake for 10 to 12 minutes until edges and centers are set. Cool on the pan for 5 minutes before transferring to a rack to finish cooling completely.

In a small bowl, whisk together icing ingredients. Spread or drizzle over each cooled cookie.