1. adjust oven racks to upper- and lower-middle positions and heat oven to 350°. grease cookie sheets or line with parchment paper.
2. whisk flour, cream of tartar, baking soda, and salt together in medium bowl; set aside.
3. either by hand or electric mixer, cream butter, shortening, and 1 1/2 cups of sugar until combined, 1 to 1 1/2 minutes with electric mixer set at medium speed.
4. scrape down sides of bowl with rubber spatula. add eggs. beat until combined, about 30 seconds.
5. add dry ingredients and beat at low speed until just combined, about 20 seconds.
6. combine sugar-spice mix in a shallow bowl. working with scant 2 tablespoons of dough each time, roll dough into 1 1/2-inch balls. roll balls in cinnamon sugar and place on cookie sheet, spacing them 2 to 2 1/2 inches apart.
7. bake, reversing position in oven halfway through baking time (from top rack to bottom and front to back), until edges of cookies are beginning to set and centers are soft and puffy, 9 to 11 minutes. let cookies cool on cookie sheet 2 to 3 minutes before transferring to cooling rack with wide spatula.