Preheat oven to 350ºF. Line a baking sheet with parchment paper.
In a large mixing bowl or stand mixer cream together the butter, sugar and brown sugar. Add in the egg, vanilla and eggnog. Continue to mix until well combined and a soft, creamy mixture is formed.
In a separate mixing bowl whisk together the flour, baking soda, salt, cinnamon and nutmeg until well combined.
Add the flour mixture to the butter mixture and mix until a soft dough forms.
Using a cookie scoop or spoon, drop the cookies onto the baking sheet. With the back of a drinking cup, press the cookies until they are 1/4 inch thick. If the cup sticks to the cookies, grease with a little oil or butter.
Bake the cookies for 8-10 minutes, until golden brown around the edges. Place on a cooling rack to cool.