Whisk the flour, baking powder, baking soda, salt, nutmeg, and cinnamon in a medium bowl.
Cream the softened butter, granulated sugar, and brown sugar in a large bowl until smooth and fluffy.
Add the eggs and vanilla extract to the butter mixture and mix until fully combined.
Pour in the eggnog and mix again until the batter becomes creamy.
Add the dry ingredients to the wet ingredients and mix until a soft dough forms.
Cover the bowl and chill the dough in the refrigerator for at least one hour.
Preheat the oven to 350°F after the dough has chilled.
Line two baking sheets with parchment paper.
Scoop tablespoon-sized portions of dough and shape them into small balls.
Roll each dough ball thoroughly in powdered sugar until fully coated.
Place the coated dough balls on the baking sheets, leaving about two inches of space between them.
Bake the cookies for 10 to 12 minutes, or until the edges look set and the tops have formed crinkles.
Remove the baking sheets from the oven and let the cookies rest for five minutes.
Transfer the cookies to a wire rack and cool completely before serving.