Heat oven to 350 degrees F. Line two baking sheets with parchment paper; set aside.
In a medium bowl, whisk together flour, cream of tartar, baking soda, and salt; set aside.
In the bowl of a stand mixer fitted with a paddle attachment, cream the butter, shortening and brown sugar at medium speed until light and fluffy, about 2 minutes. Scrape down the sides of the bowl with a rubber spatula as needed. Add the eggs and vanilla and beat at medium speed until combined, about 30 seconds. Add the dry ingredients and beat at low speed until just combined, about 30 seconds, scraping down the bowl as needed.
Place the sugar and cinnamon for rolling in a shallow bowl. Roll a heaping tablespoon of dough into a 1½-inch ball between moistened palms, roll the ball in the sugar mixture, and then place it on the prepared baking sheet. Repeat with the remaining dough, moistening your hands as necessary and spacing the balls about 2 inches apart
Bake until center is just set and begin to crack, 10 minutes, rotating the baking sheets halfway through. Cool the cookies on the baking sheets about 5 minutes; using a wide metal spatula, transfer the cookies to a wire rack and cool to room temperature.