Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper, silpat liners or grease with cooking spray. Set aside.

In a medium bowl, whisk together the flour, baking powder, salt, nutmeg and cinnamon. Set aside.

In a large bowl, whip the butter, granulated sugar and brown sugar together with an electric mixer (handheld or stand) until light and creamy, one minute or so. Add the egg yolks and mix until combined. Add the vanilla, rum extract and eggnog and mix on low speed (it will splash a bit) until just combined.

Add the dry ingredients and mix again until just combined. Using a cookie scoop or two spoons (the dough will be very soft), scoop the dough into 1-2 tablespoon-sized mounds (I use a #40 cookie scoop) and place a couple inches apart on the baking sheets.

Bake the cookies for 12-13 minutes. They shouldn't be browned on the sides at all if you want them to stay really soft; they'll have flattened into a nice cookie shape and will be just slightly puffed.

Let the cookies rest on the baking sheets out of the oven for a couple minutes before removing them to a cooling rack to cool completely.

For the frosting, whip the butter until light and fluffy, 1-2 minutes. Add the eggnog, vanilla extract and rum extract. Mix to combine (again, be aware it might splash a bit). Add the powdered sugar and whip the frosting until very light and creamy, 2-3 minutes. Add additional eggnog as needed if you want to thin the frosting a bit.

When the cookies are cool, spread frosting evenly on each cookie. Dust lightly with nutmeg.