In a mixing bowl, whisk together the flour, baking powder, salt, nutmeg and cinnamon for until well blended, set aside.
In the bowl of an electric stand mixer fitted with the paddle attachment, 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 extract, rum extract and eggnog. With mixer set on low speed, slowly add in dry ingredients and mix just until combined.
Scoop dough out by the heaping tablespoonfuls and drop onto parchment paper lined baking sheets, spacing cookies 2-inches apart. Bake in preheated oven 12-15 minutes. Allow to rest on baking sheet several minutes before transferring to a wire rack to cool. Cool completely then frost with Eggnog Frosting and sprinkle tops lightly with nutmeg.
In the bowl of an electric stand mixer fitted with the paddle attachment, whip butter until very pale and fluffy. Add in rum extract and 3 Tablespoons eggnog and mix in powdered sugar. Add additional eggnog to reach desired consistency.