In a small bowl, whisk together 1/2 cup eggnog and the flaxseed. Set aside for at lest 10 minutes, to thicken slightly.
In a medium bowl whisk together the flour, baking powder, cinnamon, nutmeg, and salt. Set aside.
In the bowl of a stand mixer, or using a large bowl and a strong hand mixer, cream together the butter and brown sugar on medium speed for 3 minutes, using a spatula to scrape down the sides of the bowl as needed.
Add the eggnog/flaxseed mixture and vanilla extract. Continue mixing for an additional 1 minute.
Add the flour mixture, 1/3 at a time, mixing just until combined after each addition.
Set the bowl with the finished dough inthe refrigeerator to chill for 30 minutes.
Remove the dough from the refrigerator. Working quickly, use your hands to roll the dough into 1-inch balls. Arrange on the baking sheets at least 2 inches apart.
Working in batches, bake for 12 minutes, until lightly golden. Set the baking sheets that are not going into the oven right away in the refrigerator until ready for their turn in the oven. Remove the cookies from the oven. Leave the cookies on the baking sheet to set for 5 minutes then remove them to a cooling rack to cool completely. Repeat with the remaining cookie dough.