Preheat your oven to 350°F (175°C). Line 2 large baking sheets with parchment paper to prevent over-browning and for easy cleanup.

In a medium bowl, whisk together the flour, cream of tartar, baking soda, salt, 2 teaspoons cinnamon, 1 teaspoon ginger, 1 teaspoon cardamom, 1/4 teaspoon cloves, and 1/4 teaspoon nutmeg until the spices are evenly distributed.

In a large mixing bowl or stand mixer fitted with the paddle attachment, beat the softened butter, 1 1/4 cups granulated sugar, and 1/4 cup packed light brown sugar on medium speed for 2–3 minutes, until light and fluffy. Scrape down the sides of the bowl as needed.

Beat in the eggs one at a time, mixing well after each addition. Add the vanilla extract and mix again until the mixture looks creamy and slightly thick.

With the mixer on low speed, gradually add the flour and spice mixture. Mix just until no dry streaks of flour remain. If the dough feels very sticky, let it rest for 5 minutes so the flour can hydrate and the dough can firm up slightly.

Cover the bowl and refrigerate the dough for 20–30 minutes to help control spreading and intensify the chai flavor.

In a small bowl, stir together 1/4 cup granulated sugar, 1 teaspoon cinnamon, 1/2 teaspoon ginger, 1/2 teaspoon cardamom, and a pinch of cloves until well combined.

Scoop the chilled dough into 1 1/2-tablespoon portions (about the size of a golf ball). Roll each portion into a smooth ball, then roll generously in the chai-cinnamon sugar to coat. Place on the prepared baking sheets, spacing about 2 inches apart.

Bake one sheet at a time for 9–11 minutes, or until the edges look set and the centers are puffed but still soft. Do not wait for the cookies to brown deeply; they will continue to firm up as they cool.

Let the cookies cool on the baking sheet for 5 minutes, then transfer them to a wire rack to cool completely. If desired, sprinkle a little extra chai-cinnamon sugar on top while they are still warm.