Preheat oven to 375°F. Line two large cookie sheets with parchment paper or a silicone baking mat. Set aside.
Whisk the flour, baking powder, and baking soda together in a medium bowl.
In a separate medium bowl, whisk together the granulated sugar, ground cinnamon, ginger, cardamom, allspice, salt and pepper. Remove 1/3 cup of it to a small bowl for later when you’re ready to roll the cookies.
In a large bowl using a hand mixer or stand mixer fitted with the paddle attachment, beat the room temperature butter and granulated sugar with the spices on high speed until smooth and creamy, 2-3 minutes. Do not skip this step.
Add the egg, egg yolk and vanilla. Beat on medium-high speed until combined, another 1-2 minutes, until the yellow streaks are gone and the dough is light and fluffy. Scrape down the bottom and sides of the bowl with a rubber spatula.
With the mixer running on low speed, slowly add the dry ingredients, beating well after each addition. The dough should be thick.
Roll the cookie dough into balls, 1.5 Tablespoons each. Roll them into the chai-sugar topping and arrange them 2-3 inches apart on the prepared baking sheet.
Bake the cookies for 10 minutes. They will be soft and puffy. Allow cookies to cool for 5 minutes on the baking sheet then transfer to a wire rack to cool completely
While they’re cooling, make the frosting. Mix the powdered sugar, eggnog or heavy cream and nutmeg together in a medium bowl. Spoon the icing over the cooled cookies and allow to set.