Preheat oven to 375°F. Line 2 large rimmed baking sheets with parchment paper. Whisk all-purpose flour, whole-wheat flour, lemon zest, cream of tartar, baking soda and salt together in a small bowl.
Beat butter and ¾ cup sugar in a large bowl with an electric mixer on medium speed until pale and fluffy, 2 to 3 minutes. With the mixer running, add egg and vanilla, beating until just combined. Reduce speed to low and gradually add the flour mixture, beating until just combined.
Place the remaining 2 tablespoons sugar in a small bowl. Using a 1 ½-inch scoop, portion the dough into about 20 pieces. Shape each piece into a ball and roll in the sugar to coat. Shake off any excess sugar and place the balls 2 to 3 inches apart on the prepared baking sheets.
Bake 1 sheet at a time until the cookies are lightly golden brown around the edges and set in the center, 11 to 12 minutes. Let cool on the baking sheet for 2 minutes, then transfer to a wire rack to cool completely, about 20 minutes.
