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

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

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

Add the egg to the butter mixture and mix just until combined. Add the cider and combine, scraping the sides and bottom of the bowl as needed.

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

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

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

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