Preheat the oven to 350 degrees. Line a baking sheet with a silpat mat.
Stir the flour, baking powder, salt, cinnamon, nutmeg, and cloves together in a bowl until well combined.
Beat the softened butter with the white sugar and brown sugar until creamy. Add the egg yolk, eggnog, and vanilla; beat until creamy.
Slowly add the flour mixture to the butter mixture until combined. Place into the refrigerator for 10-15 minutes to harden a bit. Scoop spoonfuls of dough and roll into small balls then place on the silpat mat lined baking sheet, spacing them 2 inches apart.
Place into the oven and bake for 9-11 minutes. Let the cookies rest on the baking sheet for a few minutes before moving them to a wire rack to finish cooling.
Make the frosting by beating the softened butter together with the powdered sugar and eggnog until creamy and smooth. Once the cookies have completely cooled, frost the cookies with the eggnog frosting. Grate a little fresh nutmeg on top of each cookie. Serve with ice cold milk, if desired. Enjoy.