Preheat oven to 400 degrees F (200 degrees C). Grease 1 cookie sheet.
In a large bowl, combine cornmeal, flour, and salt. In a separate bowl, beat the egg together with the oil. Stir in the chicken broth and parsley. Gradually add the egg mixture to the flour mixture, stirring to combine and make a soft dough. Working on a lightly floured surface, lightly knead dough. Roll out to a thickness of 1/2 inch. Cut into desired shapes with cookie cutters. Place cookies one inch apart on the prepared cookie sheet.
Bake in preheated oven for 15 minutes or until firm.
