For the eggnog sugar cookies:

1. Preheat the oven to 325 degrees F and line two baking sheets with parchment paper.
2. In a medium bowl, combine the cake flour, baking powder, baking soda, and salt. Set aside.
3. In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter, granulated sugar, and powdered sugar for 2-3 minutes until light & fluffy.
4. Beat in the egg, vanilla, and rum extract.
5. Add half of the dry ingredients and mix until just combined.
6. Mix in the eggnog, then the rest of the dry ingredients until just combined.
7. Using a 2 tbsp cookie scoop, place the cookie dough on the prepared baking sheets about 2 inches apart. Use one finger to pat them down into smooth balls.
8. Bake the cookies for about 12 minutes or until the edges are barely golden. Immediately after they come out of the oven, use a large round cookie cutter or glass to scoot the edges and form a perfectly round cookie.
9. Allow to cool completely on the baking sheet.

For the eggnog frosting:

1. In the bowl of a stand mixer fitted with the paddle attachment, cream the butter until smooth.
2. While mixing on low speed, add the sifted powdered sugar a little at a time.
3. Scrape down the bowl, then add the eggnog, extracts, and salt, and continue mixing on low speed until smooth and no air pockets remain.

For decorating:

1. Use a 1 tbsp cookie scoop to portion the frosting onto each cookie.
2. Spread the frosting with a spoon, then sprinkle each cookie with nutmeg. Enjoy!