Heat the extra-virgin olive oil in a cast iron skillet or large pan over medium heat. Season the chicken thighs with salt, pepper, to taste, and the paprika. Brown the chicken for a couple minutes on each side, then add the chorizo and brown for a couple minutes. Add the onions and garlic and cook for 5 minutes more. Stir in the wine to deglaze the pan, then add the tomatoes, peppers and parsley. Reduce the heat to a simmer.
In a medium pot, bring the stock to a boil over high heat. Slowly add the polenta and whisk until thickened, about 2 to 3 minutes. Stir in the butter and cheese, then spoon the polenta into shallow bowls and make a well in the center. Fill the polenta-lined bowls with the stew and serve.