Whisk the flour, baking powder, salt, nutmeg, and cinnamon together in a medium bowl. Set aside.
Using stand mixer fitted with the flat beater attachment, beat together the butter and sugars until pale and fluffy. Add in egg yolks, one at a time, mixing after each addition. Mix in vanilla, rum extract, and eggnog until combined.
With mixer on low, slowly add in dry ingredients and mix until just combined. Remove bowl from stand mixer, cover, and refrigerate at least 3 hours or overnight. An overnight refrigeration is suggested if you can do it!
Preheat oven to 350°F. Scoop out tablespoon sizes of cookie dough and place onto parchment-lined baking sheet about 2 inches apart.
Bake for 14-15 minutes or until cookies are golden brown on edges and cooked in the center. Remove from oven and let cool completely before frosting.