In the bowl of a stand mixer with the paddle attachment, beat butter until pale, about two minutes.

Add sugar and beat one minute.

With mixer running on low, add one egg yolk at a time and then add the eggnog and rum and mix to combine.

In a medium bowl, whisk the flour, baking powder, salt, nutmeg, cinnamon and allspice and with mixer running on low, slowly add in the dry ingredients.

Mix just to combine, scrape and mix one more time.

Wrap the dough in plastic and chill two hours.

Make the frosting by creaming the butter and sugar in the bowl of a stand mixer with the paddle attachment.

Add rum, eggnog, nutmeg and cinnamon and mix until creamy and smooth. Set aside at room temperature.

Line a few cookie sheets with parchment paper.

Preheat oven to 325 degrees F with rack in upper third of oven.

Flour the counter and place half the dough on the flour and roll to ¼ inch thick.

Use holiday cutouts and place cutout cookie shapes on one of the prepared cookie sheets. The cookies do not spread much so they can be as close as a half inch from each other.

Bake one pan at a time for 12 minutes until the bottoms are browned and the tops a pale light brown.

Repeat for remaining dough reusing dough scraps as you go. I reused dough scraps four times.

Cool on racks then frost. If the frosting is too stiff, whisk in a small amount of milk to loosen it up.

While still wet, sprinkle on holiday sprinkles.