Preheat oven to 375.
Using a stand mixer with a paddle attachment, cream 2 sticks of butter and 1.5 c granulated sugar together on medium speed for 1-2 minutes.
Add in egg, egg yolk & vanilla. Mix until just combined & scrape the sides of the bowl with a spatula.
In a separate small bowl, mix chai spices together & set aside. (You'll use part for the dough and part for the frosting.)
In a separate mixing bowl, lightly whisk the flour, baking soda, baking powder, 3.5 tsp of the chai spices, and salt together.
Turn the mixer on low speed and gradually add in the flour mixture to the wet. Mix until just combined, scraping the sides of the bowl to make sure everything is evenly incorporated.
Roll into 12 dough balls, roll dough balls into extra granulated sugar, and set them on the pan until you've got your traditional dozen on the pan. (See notes on baking pans.)
Bake for 8 minutes at 375.
Remove from oven, allow to cool on the pan for a couple of minutes, and then remove from the pan onto a cooling rack. Repeat with other half of cookie dough. Allow cookies to cool before making & adding the frosting.