1-First: preheat the oven to 350°F (175°C) and line baking sheets with parchment paper or a silicone mat. In a bowl, whisk together the flour, baking powder, salt, nutmeg, and cinnamon for about 30 seconds and set aside. Using an electric mixer with a paddle attachment, cream the butter with the granulated and brown sugars until pale and fluffy.

2-Add the egg yolks one at a time, mixing until just combined after each addition. Stir in the vanilla extract, rum extract, and eggnog. Gradually add the dry ingredients on low speed and mix just until combined. Scoop the dough by heaping tablespoonfuls onto the prepared baking sheets, spacing approximately 2 inches apart.

3-Baking and Finishing Touches: Bake for 11 to 13 minutes, then allow the cookies to rest on the baking sheet for a few minutes before transferring to a wire rack to cool completely. For the frosting, whip butter until very pale and fluffy with an electric mixer, then add rum extract and 3 tablespoons of eggnog before gradually adding powdered sugar until the desired consistency is reached. Frost the cooled cookies and lightly sprinkle with nutmeg.