Cream butter and sugar in a large bowl using a hand or a stand mixer. Add egg, baking soda, cream of tartar, and vanilla and mix well. Mix in the cornmeal and all purpose flour until smooth.
Line a cookie sheet with parchment paper or a silpat baking mat. Scoop 2-3 tablespoon cookie balls onto the cookie sheet. There is no need to space them out, this is just for chilling. Chill dough at least 30 minutes!
Preheat oven to 350°F. Place some granulated sugar in a bowl and roll each ball to coat. Spread out your cookies onto 2-3 cookie sheets (depending on size). Bake for 9-13 minutes, until just browned around the edges. Don't over bake - they'll finish baking as they cool. Actual baking time depends on the size of the cookies. Cool completely before removing from cookie sheets. Store in an airtight container for up to 3 days or freeze for up to 1 month.
Cornmeal Sugar Cookies https://www.yellowblissroad.com/cornmeal-sugar-cookies/