Preheat the oven to 350 degrees. Line cookie sheets with parchment and set aside.
Use a stand mixer or hand-held mixer to combine the butter and brown sugar. Cream until smooth and lighter in color.
Add in the egg and molasses. Mix until combined.
Add the flour, ginger, cinnamon, cloves, nutmeg, baking soda, and salt. Mix until thoroughly combined - stopping and scraping down the sides as you go.
Using a tablespoon or a small ice cream scoop, scoop out golf-ball-sized balls of dough onto the prepared cookie sheets, 1 inch apart.
Bake in the preheated oven for 8 minutes.
Immediately upon removing from the oven, use the bottom of a spatula to flatten each cookie to about ½ of an inch in thickness.
Allow cookies to cool on the sheet for 1 minute, then remove to a cooling rack. Allow to cool completely.
While the cookies are cooling, make the frosting. In a large mixing bowl, combine the softened butter and cream cheese. Beat until smooth.
Add the vanilla (or eggnog!) and about half of the powdered sugar. Mix until combined.
Add in the remaining powdered sugar and mix thoroughly. Scrape the sides and mix again.
Transfer the frosting to a piping bag fitted with a large star tip.
Once the cookies are cool, pipe a small spiral in the center of each cookie. Sprinkle with nutmeg to taste.