Add the butter and sugars to the bowl of a stand mixer fitted with the paddle attachment and beat until smooth and creamy, 2-3 minutes.
Add the eggnog, egg, and vanilla and beat until well combined. It may look curdled, that's okay!
Add the flour, cream of tartar, baking soda, cinnamon, nutmeg, and salt and beat until well combined.
Cover the bowl and place in the fridge for 30 minutes. Meanwhile, preheat the oven to 350℉ and line a large baking sheet with parchment paper. Also, stir together the sugar, cinnamon, and nutmeg in a small bowl and set aside.
After chill time, scoop out 2 inch balls of dough, then roll them into balls. Roll them evenly in the sugar spice mix and place the cookies on the parchment paper 2 inches apart.
Bake in the preheated oven for 14-16 minutes or until the cookies are just starting to brown around the edges. Allow to cool, then serve!