In the bowl of your mixer, place your butter and sugars, then mix until well combined, and light and fluffy.
Mix in your egg yolks, one at a time, beating well between each addition. One of my yolks broke while I was separating my eggs, but that's no big deal. I just added in the whole yolk first, then scrapped my bowl out into my mixing bowl.
Once your egg yolks are well mixed in, add your vanilla and rum extracts, and, again, mix well.
Now the fun part comes in! Add in your eggnog, and mix well (don't worry, the mixture will look very lumpy, almost curdled, but its fine!); after your eggnog has been well mixed, slowly add in your sifted dry ingredients, and mix until just combined.
After they come out of the oven, let them sit on the sheet for about 6-7 minutes, before moving them (carefully) to a cooling rack. These are pretty delicate cookies, so be careful. As they cool, they become more firm, so don't worry about that.
After the cookies have cooled completely, you can frost the cookies. This frosting is very easy to make, and really sets these cookie apart from any other! It's so good! To start off with, put your butter into your mixing bowl, and whip it until it is a light yellow color.
Slowly sift in your powered sugar, 1 C at a time, mixing well between each addition.
Once all of your sugar has been added, the butter and sugar will have formed a very paste. Add in the eggnog, 1 TBS at a time, until you have the consistency you like. I ended up using 5, but I wanted a pretty spreadable frosting, personally.
These look great as-is, but add a light dusting of freshly grated nutmeg, and these cookies really pop! To set up the frosting, just set them in the fridge for a bit, and then these are stackable, without sticking to each other. These are a lot of fun to make, and are sure to be snapped up quickly at any gathering you may go to (or, even around your house!), so I really hope you give 'em a go and make some! Yum!