Preheat oven to 350 degrees. In a mixing bowl whisk together flour, baking powder, salt, nutmeg and cinnamon for 30 seconds and set aside. In a bowl of an electric stand mixer whip together butter, granulated sugar and brown sugar until pale and fluffy.
Mix in egg yolks one at a time blending just until combined after each addition. Mix in vanilla, rum extract and egg nog. With mixer set on low slowly add dry ingredients and mix just until combined.
Scoop dough out by heaping tablespoons and drop onto parchment paper lined baking sheets spacing cookies 2 inches apart. Bake 11 - 13 minutes. Allow to rest on sheets several minutes before transferring to wire rack to cool. Cool completely then frost with Eggnog Frosting and sprinkle tops lightly with nutmeg.
For Frosting? In the bowl of a electric stand mixer whip butter until pale and fluffy. Add in rum extract and 3 tablespoons eggnog and mix in the powdered sugar. Add additional eggnog to reach desired consistency.