Grease a 9x9" baking dish with cooking spray or olive oil.
Bring 3 cups of water to a boil in a large stock pot. Slowly whisk in polenta to avoid lumps. Cook on low for 10 minutes.
Stir in the heavy cream, salt, black pepper, grated Oaxaca or Mozzarella cheese. Add the chicken (optional) and stir.
Simmer for another 15 minutes more. If it gets too thick you can thin it out with more water or chicken stock to your liking. Season to taste and take off the heat.
Pour immediately into prepared pan and spread for even layer. Freeze 15-20 minutes or 1 hour in the refrigerator.
Preheat the oven to 425°F. Using a rubber spatula, run it along the sides of the pan to loosen polenta. Flip the polenta onto a cutting board and cut into 1/4 inch thick "fries".
Place the fries on a parchment paper lined baking sheet and spray "fries" with olive oil or cooking spray then season with salt, and pepper. Be sure the fries are in an even layer. Transfer to the oven and bake for 15 minutes, then carefully flip to brown other side. Bake for 15 minutes more, until extra crispy and golden brown.
Let cool 5 minutes before serving with Salsa Verde as dipping sauce.