Preheat oven to 350 degrees. Line a cookie sheet with parchment paper.
In a mixing bowl, add in the butter and sugar. Beat with a hand mixer until light and fluffy. It will take about 2 - 3 minutes.
Add in the eggnog and mix until combined. Scrape down the sides of the bowl.
Add in the egg and vanilla extract and mix until incorporated.
Add in the all the dry ingredients and beat until the flour is just incorporated.
Scoop out the cookie dough using a large cookie scoop.
Place in the oven and bake for 11 - 14 minutes until done. The edges will be golden brown.
Place on a cooling rack and let cool before adding the glaze.
Glaze
In a small bowl, whisk together the eggnog and powdered sugar.
Spoon the glaze onto the cooled cookies.
Before the glaze dries, lightly dust with cinnamon. I place a very small amount of cinnamon into a small strainer and give it a tap over each cookie. Be sure to hold it high above the cookies to give it a spread out dusted look.