Preheat the oven to 350F (180C) or 325F (170C) on a convection oven (some ovens do this automatically). Line cookie sheets with parchment paper or silicone baking mats.
Whisk together the flour, nutmeg, cinnamon, baking soda, and salt in a medium-sized bowl. Set aside.
In a large bowl, beat together the butter, granulated sugar and brown sugar until fluffy.
Beat the 2 egg yolks (remember not to use the whole egg), vanilla extract and rum extract into the butter mixture.
With the mixer on a low speed, beat the eggnog into the butter mixture.
Then mix the flour mixture into the butter and eggnog mixture, starting with your mixer on a low speed and gradually increasing until combined.
Scoop the dough into balls with about 1 to 1.5 tablespoons of dough each (I used a medium cookie scoop). Roll the dough into balls and place about 2 inches apart on the lined cookie sheets. For slightly flatter cookies, press the balls down slightly.
Bake 1 sheet at a time on a middle rack in the preheated oven for about 8-11 minutes or until the tops look set and the edges are just starting to become golden.
Remove from the oven and cool on the cookie sheet for at least 10 minutes before transferring to a cooling rack.