Preheat oven to 350 degrees.
Combine butter and both sugars in a bowl.
Beat on a medium-low speed, using either the paddle on a stand mixer or a hand mixer for 4 minutes.
Add eggs one at a time, beat after each addition, scraping sides to combine.
Add vanilla to dough, and mix until combined.
Add flour, cornmeal, baking soda, and salt, stirring until combined.
Line a baking sheet with a piece of parchment paper, then scoop heaping tablespoons of dough onto the prepared tray.
Bake for 10-12 minutes or until the edges are golden brown.
Allow to cool for 4 minutes, then transfer to a baking rack to cool completely.