Add the flour, baking powder, nutmeg, cinnamon, and salt to a medium-sized mixing bowl. Whisk to combine.

Using either a stand mixer or a large mixing bowl and handheld mixer on medium-high speed, beat the softened butter for 30-45 seconds.

Add the granulated and dark brown sugar. Beat for 1-1½ minutes until well combined.

Lower the mixer speed to medium-low speed. Add the eggs, one at a time, until incorporated, and no yellow streaks remain.

Add the vanilla and rum extract and mix just until combined.

Add the flour mixture, 1 cup at a time, alternating with eggnog. Mix just until the ingredients are well incorporated and smooth. Cover the dough and chill in the refrigerator for at least 1 hour.

Just before you are ready to bake the cookies, preheat the oven to 350°F. Line 2 baking sheets with parchment paper.

Remove the cookie dough from the refrigerator. Use a 1½-tablespoon cookie scoop to scoop out the dough. Place the dough 2 inches apart. Bake for 10-12 minutes or until the edges are golden brown. Remove the cookies from the oven and allow them to cool on the baking sheet for 2-3 minutes before transferring to a cooling rack to cool completely.

Using either a stand mixer or medium-sized mixing bowl and a handheld mixer on medium speed, beat the softened butter for 45 seconds to 1 minute.

Lower the mixer speed to medium-low. Alternate adding powdered sugar and eggnog. Continue mixing until the frosting is well incorporated and smooth.

Spoon the frosting into either a disposable piping bag fitted with a star-shaped tip (I used Wilton tip 1M) or a quart-size ziplock bag with an edge snipped off.

Use gentle, steady pressure to pipe the frosting over the surface of the cookie, starting from the outside edge and working your way to the center of the cookie (so it will look like a spiral). Sprinkle a light dusting of the ground nutmeg over the tops of the frosted cookies.