Prepare the filling by adding olive oil to a large skillet over medium-high heat. Stir in onions, bell peppers and garlic. Stir often, cooking about 10 minutes until softened.
Remove from heat. Stir in cumin, chili powder, salt and pepper.
Add chicken, black beans and shredded cheeses to the vegetables and mix to combine.
Preheat oven to 350° with a 12 inch cast iron skillet in the oven as it preheats.
In a large bowl, combine cornmeal, flour, baking soda and salt.
Add milk, eggs, bacon grease (or vegetable oil), and cream corn if using. Mix to combine.
Carefully remove cast iron skillet from the oven and coat with bacon grease or vegetable oil, about 1 tablespoon.
Pour half of cornbread batter into the skillet, spreading to the edges.
Top with filling in an even layer.
Top with remaining cornbread batter, spreading over the top.
Bake for 35- 45 minutes or until a toothpick inserted comes out clean.
Remove from oven, slice and serve immediately.