Preheat oven to 350ºF. Line baking sheets with parchment paper
Cream together butter and sugars. Add in egg, vanilla and eggnog. Mix until combined and smooth.
In a separate bowl whisk together the dry ingredients.
Pour the dry ingredients into the bowl with the butter mixture and mix with an electric mixer or in a stand mixer until a soft dough is formed.
Using a cookie scoop or spoon, scoop the dough onto the baking sheet. Use the back of a drinking glass to press the cookies flat before baking. If the glass sticks to the dough, spray with cooking spray.
Bake the cookies for 8-10 minutes, until golden brown. Place on a cooling rack to cool.
Eggnog Frosting
In the bowl of a stand mixer or with a hand mixer. Beat the butter until smooth. Add in the eggnog and vanilla and mix. Pour in the powdered sugar and mix for another minute, scrapping down the sides until the frosting is smooth.
Spread over cooled cookies.
Mix the nutmeg and cinnamon and sprinkle over the tops of the cookies.
Notes
Store any leftover cookies in an airtight container on the counter for at least 2 days.
Eggnog cookies can be frozen after they have been baked
This is a really soft dough, if you feel that it is too sticky, you can add additional flour, one tablespoon at a time until it is easier to handle, or place covered in the refrigerator for at least 15 minutes to allow the dough to harden before scooping.