Preheat oven to 350° F. Prepare a baking sheet with parchment paper.
Add the flour, cornmeal, and salt to a bowl and whisk to combine.
In a large bowl, using a hand mixer, beat the butter and sugar until light and fluffy. Add the egg and vanilla and continue to beat until smooth. With the mixer on low, gradually add the flour mixture until combined.
Drop a heaping teaspoon of the cornmeal sugar cookie dough onto the prepared cookie sheet 2 inches apart. Press each cookie a tiny bit flat with your fingertips.
Bake for 14 to 18 minutes or until the edges are brown. Rotate the baking sheet halfway through. Transfer the cookies immediately to baking rack to cool completely!