What you have here is rather much a sugar cookie made with cornmeal and masa. As with flour cookies, they’re often seasoned with various flavorings, herbs, spices, and/or fruit. This recipe makes a somewhat soft cookie that can be firmed up with the addition of a bit more masa.
Whisk together a quarter cup of yellow cornmeal and a quarter cup of masa harina with a cup and a half of AP flour, a half teaspoon of baking powder, a half teaspoon of baking soda, and a teaspoon of salt. Beat together two sticks softened butter, a cup and a half of sugar, a quarter cup of honey, a large egg, and a teaspoon of vanilla with an electric mixer at medium speed until fluffy.
Gradually add cornmeal mixture until just combined. Form dough into a ball and refrigerate in plastic wrap for about a half an hour. Roll out to about a quarter inch, cut into rounds and bake on a lightly oiled cookie sheet on the middle rack at 350 until lightly browned.