In a bowl, cream the butter, brown sugar and sugar together until fluffy.
Add the eggs, 1/4 cup of eggnog and vanilla.
Beat until blended.
In another bowl, whisk together the flour, baking soda, baking powder, 1 teaspoon of nutmeg and cream of tartar.
Add the dry ingredients into the wet and stir until just combined.
Cover dough and refrigerate for at least 1 hour.
Preheat the oven to 350.
Prepare a cookie sheet by either greasing or lining with parchment paper or silicone mat.
Form the dough into 1" balls and place on prepared sheet.
Bake 8-9 minutes until lightly browned on edges.
Cool on cookie sheet for 10 minutes before moving to a wire rack.
Whisk together powdered sugar and 1/4 teaspoon of nutmeg.
Add eggnog 1 tablespoon at a time and stir to blend until desired consistency is reached.
Drizzle glaze over cookies and allow to set.