Position racks in the upper and lower thirds of the oven and preheat to 375 degrees F. Whisk the flour, cocoa powder, cream of tartar, baking soda and salt in a medium bowl. Beat the butter, granulated sugar and brown sugar in a large bowl with a mixer on medium speed until creamy, about 2 minutes. Increase the speed to medium high and beat until fluffy, about 2 more minutes. Beat in the egg and vanilla; reduce the mixer speed to low and beat in the flour mixture until just combined.
Combine the sanding sugar and cinnamon in a small shallow bowl. Form heaping tablespoonfuls of dough into balls with damp hands; toss in the cinnamon sugar to coat. Arrange about 3 inches apart on 2 baking sheets.
Bake, switching the pans halfway through, until the cookies are set around the edge, 9 to 11 minutes. Let cool 2 minutes on the baking sheets, then transfer to a rack to cool completely.