Preheat the oven to 350℉. Line two baking sheets with parchment or spray with cooking spray.
In a small bowl, whisk together the flour, cornstarch, salt, cinnamon, and nutmeg. Set aside.
In a large bowl or the bowl of a stand mixer, beat together the butter and powdered sugar until light and fluffy. Add the rum extract, vanilla, and eggnog, and mix to combine (it's okay if it doesn't mix together perfectly at this point). Add the dry ingredients and mix to form a thick dough.
Shape the dough into one inch balls and place 1-2 inches apart on the baking sheets. Bake 12-14 minutes, or until lightly browned on the bottom.
Remove and let cool 15 minutes, then roll in powdered sugar. Enjoy!
Storage: Place cooled cookies in an airtight container for up to 2 weeks at room temperature.Freezing: Place cooled cookies in an airtight container in a single layer. Place parchment paper between layers and store cookies in an airtight container in the freezer for up to 6 months. Thaw at room temperature.Make Ahead: This recipe does not require you to chill the dough, but if you'd like to make it ahead of time, you can refrigerate for up to 24 hours.