Preheat oven to 350 degrees F. Line a cookie sheet with parchment paper or a silicone baking mat.
Combine the white sugar, brown sugar, vanilla and butter in the bowl of your stand mixer fitted with the paddle attachment. Beat on medium low speed until the mixture is creamed, light and fluffy.
Add the eggs one at a time, continuing to beat on medium low speed.
In a separate bowl combine the flour dark cocoa powder, baking soda, and salt. Turn the mixer down to low and gradually add the dry ingredients to the wet ones, until fully incorporated.
Add in the chocolate chips until evenly distributed.
Scoop teaspoon size balls onto prepared baking sheet at least 2 inches apart and bake for 10 to 12 minutes. Let cool slightly before removing to wire rack to cool completely.
To make the Frosting:
Cream the butter in the bowl of your stand mixer fitted with the paddle attachment until light and fluffy. Add 3 1/2 cups of powdered sugar, salt and nutmeg to bowl. Turn mixer to low until the powdered sugar is absorbed and then increase the speed to medium and whip for 2 minutes.
Start by adding 2 tbsp of eggnog and continue beating the frosting. Add more eggnog to thin the frosting or more powdered sugar to thicken if needed.
Pipe the frosting onto the cooled cookies to make sandwiches.