In a medium bowl, whisk together the flour, baking powder, nutmeg, cinnamon, and salt. Set aside.
Beat sugars and butter together in a large bowl with an electric mixer or in the bowl of a stand mixer fitted with the paddle attachment until light and fluffy.
Add eggnog, egg yolks, and vanilla; beat at medium speed until smooth.
Gradually beat in flour mixture at low speed until just combined.
Cover dough and chill in the refrigerator for at least 1 hour.
Preheat the oven to 300°F (150°C). Line baking sheets with parchment paper or silicone baking mats.
Use a medium cookie scoop to portion the dough 2 inches apart onto the prepared baking sheets.
Bake in the preheated oven until edges are just golden, about 20-25 minutes.
Cool on the baking sheet briefly before removing to a wire rack to cool completely.
Once the cookies have cooled completely, prepare the icing. Add the butter, powdered sugar, and eggnog to the bowl of a stand mixer fitted with the paddle attachment or in a large bowl with an electric mixer. Beat on low speed until combined, then increase speed to high and mix for 2-3 minutes.
Spread icing onto cookies. If desired, sprinkle with sparkling sugar or additional nutmeg while the icing is still wet.
