Preheat the oven to 175C/350F. In a medium bowl, combine the cornmeal, all-purpose flour, corn flour and salt. In another medium bowl, using a hand mixer at a low speed, beat the butter and sugar until light and fluffy. Beat in the egg and vanilla until well-mixed. Beat in the dry ingredients until just combined. (You can mix by hand, as well.)
Use a small kitchen spoon to scoop and place 24 balls of dough on a baking sheet. Place your thumb in the middle of each ball and press down, making a little bowl shape in the middle of the cookies. Add preferred filling, if desired.
Bake for 8 minutes, or until the cookies are brown on the edges; rotate the baking sheet halfway through baking. Let the cookies set and cool before serving.
