Preheat oven to 350°F. Grease or spray a 2-quart baking dish (about 11 x 7-inches or 9-inch square) with cooking spray and set aside. Heat olive oil in a skillet over medium-high heat. Add the onion, bell pepper, and celery. Saute the veggies until tender, about 5-7 minutes.
In a large bowl, combine cornbread, sauteed vegetables, and cheese. Season with salt and pepper to taste.
Place half of the cornbread mixture in the prepared baking dish. Spread the chicken in an even layer over the cornbread mixture.
Whisk together the soup, broth, chili powder, paprika, cumin, oregano, and cayenne until completely combined. Taste and season with salt and pepper, if desired. Pour the soup mixture over the chicken.
Spread the remaining cornbread mixture over the chicken and gently press down to form a top crust.
Bake, uncovered, for about 30 minutes, or until hot, bubbly, and golden brown on top. If you prefer the topping more moist instead of toasty and crisp, cover the dish with aluminum foil for the first 15-20 minutes of baking time.
Garnish with chopped fresh parsley or sliced green onion and serve.