Preheat oven to 350 degrees and line baking sheets with silicone baking mat or parchment paper.
In a large bowl, whisk together the flour, baking soda, baking powder, and salt. Set aside. In a small bowl combine the sugar, cinnamon, ground ginger, cardamom, black pepper, and allspice. Measure out 1/3 cup of this spice mixture and set that aside to use to top the cookie dough.
In the bowl of a stand mixer, beat the butter and sugar spice mixture until light and fluffy. Add in the eggs and vanilla. Beat until well combined.
Add in the flour mixture, a little at a time and mix until combined.
Using a cookie scoop, form tablespoon sized dough balls and place onto prepared baking sheets. Flatten the balls slightly and using the reserved sugar spice mixture, sprinkle a bit on top of each cookie. Alternatively, you could roll the dough ball into the sugar mixture and then flatten slightly.
Bake for 10 - 12 minutes. Let cookies cool for 5 minutes on pan before moving them to a cooling rack.
To make the eggnog frosting, combine 1 1/2 cups powdered sugar, nutmeg, cinnamon, and 1/4 cup eggnog in a small bowl. Whisk until smooth. If the glaze is not thin enough to drizzle over the cookies, add a tablespoon at a time of more eggnog, until it's the desired consistency. Let the frosting set for a few minutes before storing them.