Preheat your oven to 350°F. Line baking sheets with parchment paper or spray with nonstick cooking spray.
In a mixing bowl, cream together the butter, granulated sugar, and brown sugar on medium-high speed for 2–3 minutes, until smooth.
Add in the eggs and vanilla. Mix until well incorporated.
In a separate small bowl, mix together the cinnamon, ginger, cardamom, nutmeg, cloves, and black pepper to create your chai spice blend.
Add some of the chai spice to the mixing bowl along with the flour, cream of tartar, baking soda, and salt. Mix on low, scraping the bowl as needed, until a dough forms.
Combine the remaining chai spice with sugar in a small bowl.
Scoop the dough into tablespoon-sized balls, roll in the sugar-spice mixture, and place spaced a few inches apart on the baking sheet. Bake for 10 minutes.