In a medium bowl, whisk the flour, baking powder, cinnamon, and nutmeg. Set aside.
In a large bowl with an electric mixer, combine butter and sugar until mixed well.
Add eggnog, vanilla extract, and egg yolks and beat until well combined.
Add the flour mixture and mix until no traces of flour remain.
Place cookie dough onto a sheet of waxed paper. It will be sticky. Form a log and roll in waxed paper. If it's too sticky, place in fridge for 30 minutes to firm up, then roll into a log. Chill in the freezer for 2 hours.
Preheat oven to 325 F and line insulated baking sheets with parchment paper.
Remove dough log from freezer. Cut into 1/2-inch thick slices and arrange on baking sheet an inch or so apart. If cookies are still frozen, allow to sit out for a few minutes until they are thawed.
Bake for 15 minutes. Remove from oven and allow to rest on pan for 5 minutes. Move to cooling racks to cool completely.
Prepare the Frosting
Beat the butter until creamy.
Slowly add 1 cup of the powdered sugar.
Add 4 tablespoons of the eggnog.
Mix in remaining powdered sugar.
You can use the remaining 2 tablespoons of eggnog to get your frosting to the desired consistency. (We used a total of 5 tablespoons of eggnog.)
Frost the cookies.
Dust the frosted cookies with nutmeg using a sifter.
Notes
As with most cookie doughs, you can make this dough ahead of time. Eggnog cookie dough can be stored in the refrigerator for up to 4 days or frozen for 3 months.
You can freeze completed cookies by placing cookies on a wax paper lined sheet and freezing 2-3 hours. When solid, place frozen cookies into an airtight container. Thaw at room temperature.