Whisk together cornmeal, flour, and salt. Beat butter, sugar, and vanilla with an electric mixer at medium speed, scraping down side of bowl occasionally, until pale and fluffy, about 5 minutes. Beat in egg and yolk until combined well. Reduce speed to low and add cornmeal mixture in a slow stream, mixing until just combined. Form dough into a 5-inch square and chill, wrapped in plastic wrap, until firm, about 30 minutes.
Roll out dough on a lightly floured surface with a lightly floured rolling pin into a 7-inch square (1/2 inch thick). Score dough in one direction with tines of a fork. Following scored marks, cut into 8 equal strips, then cut strips in half to form rectangles.
Bake on an ungreased baking sheet until bottoms of cookies are pale golden, 15 to 18 minutes.
Transfer to a rack to cool completely, about 1 hour.
Cookies can be made 1 day ahead and kept in an airtight container at room temperature.
