Preheat the oven to 400°F degrees. Line two baking sheets with parchment paper if you have it, or leave them ungreased if not.
In a medium bowl, stir together the flour, cocoa powder, cream of tartar, baking soda, and salt. In a large bowl, using an electric mixer, beat the butter and 1 ½ cups sugar on medium speed until light and fluffy, about 2 minutes. Scrape down the sides of the bowl. Add the eggs one at a time and beat to combine. With the mixer on low, gradually add the flour mixture and beat until combined.
In a small bowl, combine the remaining ¼ cup sugar, cinnamon, and chile powder (if using). Using heaping tablespoons, form balls of dough and roll in the cinnamon-sugar mixture. Place the balls about 3 inches apart, on the baking sheets.
Bake one sheet at a time until the cookies are set in center and begin to crack, about 10 minutes. If you want to bake the two sheets at once, make sure you have the racks spaced out in the oven in the top third and the bottom third, and rotate the baking sheets halfway during the baking. Let the cookies cool on sheets on wire racks for 3 or 4 minutes, then transfer cookies to wire racks to cool completely.
Notes
DO NOT USE MEXICAN CHILI POWDER BLEND! That has other seasonings in it, like oregano and garlic, and it’s not what you want in a cookie. You want to use pure chile powder, and it doesn’t really matter what kind. Ancho chile powder, guajillo chile powder, as long as it is a powder made from pure chiles, you are in business.