Preheat the oven to 325°F. Line a baking sheet with parchment paper. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, mix the butter, shortening, granulated sugar, and brown sugar.
Mix in eggs, honey, and vanilla.
To the butter mixture, add the flour, cornmeal, cornstarch, salt, baking powder, and baking soda. Mix until the ingredients are well incorporated.
Using a 1-tablespoon scoop, drop portions of dough onto the lined baking sheet, spacing them about 1 inch apart. Gently roll each into a ball.
Bake for 8-10 minutes. (Do not overbake these cookies. They are perfect when slightly under-done. Over-baked cookies will be dry.)
Once baked, remove the cookies from the oven and allow them to cool on a wire rack while you prepare the frosting.