Heat the oven to 375°F. Line two baking sheets with parchment. Whisk the flour, cream of tartar, baking soda and salt in a medium bowl.
Beat the butter and 3/4 cup sugar with an electric mixer on medium speed until light and fluffy, about 3 minutes. Beat in the egg and vanilla.
Add the flour mixture and mix on low just until no dry streaks remain; the dough will be soft but scoopable.
Stir the 2 tablespoons sugar and cinnamon in a small bowl. Scoop the dough into 1 1/2-tablespoon balls, roll each in the cinnamon sugar, and set 2 inches apart on the sheets.
Bake one sheet at a time on the center rack for 9-11 minutes, until the edges are set and the centers still look slightly underdone. Cool on the sheet for 5 minutes, then transfer to a rack. Repeat with the second sheet.