Preheat your oven to 350°F (180°C) or 325°F (170°C) for convection ovens. Line your cookie sheets with parchment paper or silicone mats.

Whisk together the flour, nutmeg, cinnamon, baking soda, and salt in a medium bowl. Set this mixture aside.

Beat together the softened butter, granulated sugar, and brown sugar in a large bowl until fluffy. This should take about 2-3 minutes.

Incorporate the egg yolks, vanilla extract, and rum extract into the butter mixture. Beat until combined.

Mix in the eggnog on low speed, ensuring it blends into the creamy butter mixture.

Combine the flour mixture into the butter and eggnog mixture, starting on low speed until just combined.

Scoop the dough into balls with about 1 to 1.5 tablespoons each. Place them about 2 inches apart on your lined cookie sheets.

Bake one sheet at a time on the middle rack for about 8-11 minutes.

Cool the cookies on the baking sheet for at least 10 minutes before transferring them to a cooling rack.

Beat the butter for the frosting until smooth and creamy.

Add in 2 cups of powdered sugar, nutmeg, salt, and rum extract to the whipped butter. Start mixing on low speed.

Incorporate the remaining powdered sugar, alternating with eggnog until the frosting reaches desired thickness.

Frost the fully cooled cookies using a flat knife. Optionally, sprinkle extra nutmeg on top.