Preheat oven to 375 degrees F (190 degrees C). Whisk together the flour, corn flour, and cornmeal in a mixing bowl. Lightly grease two baking sheets.

Place the peanut butter in a microwave safe dish, and cook in the microwave a few seconds at a time until the peanut butter has liquefied. Stir the peanut butter, water, vegetable oil, and egg into the flour mixture until a stiff dough forms. Roll out on a floured surface and cut into treat shapes with a cookie cutter. Place the treats onto the prepared cookie sheets.

Bake in the preheated oven until golden, 10 to 12 minutes. Allow the treats to cool on the baking sheets for 5 minutes before removing to a wire rack to cool completely. Store in an airtight container.