Preheat the oven to 350 degrees F and line a baking sheet with parchment paper, set aside. In a large mixing bowl, add the flour, baking soda, baking powder, cinnamon, nutmeg, and salt.
Stir until well combined, set aside.
In a separate mixing bowl, cream together sugar and softened butter until light and fluffy.
Add the egg and vanilla extract to the butter mixture and mix until combined.
Add the ⅓ cup eggnog to the butter mixture and mix until combined.
Next, add about half of the dry ingredients into the eggnog mixture, stir until combined. Add the other half and mix until well combined and a formable dough is formed.
Roll the dough into 2-inch balls and place on the baking sheet.
Flatten each slightly with your hand and bake in the preheated oven for 13-14 minutes or until the edges are just becoming golden brown.
Remove from the oven and allow to completely cool.
Make the eggnog glaze by combining the glaze ingredients in a small bowl and mix until combined.
Drizzle the glaze over the cooled cookies, sprinkle with your choice of sprinkles or more nutmeg if desired, allow the icing to set and serve!