Preheat the oven to 350 F (177 C). In a large bowl sift or whisk together the flour, cream of tartar, baking soda, salt, cinnamon, ginger, and cloves.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and sugar together until light and fluffy, 1-2 minutes.
Add the eggs one at a time, beating until they are fully incorporated. Add the vanilla and scrape down the sides of the mixing bowl.
Add the dry ingredients and mix on low speed until well-blended. Stop the mixer when just a few streaks of flour remain, and finish mixing by hand with a rubber spatula.
If you have the time, I think these cookies are better after the dough has chilled for 2 hours--they will be easier to roll, and they will be puffier and not spread as much. However, if you're pressed for time, you can make them right away--they'll just spread and flatten more.
Combine the sugar and cinnamon used for rolling the cookies in a bowl. Scoop small spoonfuls of cookie dough and roll them between your palms to get nice balls. Roll them in the spiced sugar, and place them on cookie sheets covered with parchment paper.
Bake at 350 for 10-12 minutes, until they are puffed, lightly golden, and crinkly on top. Cool on cookie sheets for 2-3 minutes, then transfer to a wire rack to cool completely.