Combine the seasoning mix ingredients in a small bowl.
In a 12-inch skillet over high heat, combine the butter with 2 tablespoons of the oil. As soon as the butter melts, add the onions, all the chile peppers, and 1 tablespoon plus 2 teaspoons of the seasoning mix. Stir well, then cook, stirring occasionally, until the vegetables begin to brown, about 6 to 8 minutes. Remove from the heat and set aside to cool to room temperature. The mixture should be a golden tan color, the onions a medium tan brown, and the peppers dark red and dark green. The vegetables retain a slight crunch.
Preheat the oven to 350 degrees F.
While the vegetables are cooling, make the cornbread batter. Combine the corn flour, all-purpose flour, sugar, cornmeal, baking powder, and the remaining seasoning mix in a large bowl. Add the egg, milk, melted butter, 1/2 cup each of the grated Cheddar and Monterey Jack, and the vegetable mixture. Mix until just combined.
Pour the remaining 2 tablespoons oil into a 12-inch cast-iron skillet. Make sure that the oil covers the entire bottom of the skillet; lift and roll the skillet if necessary. Heat the oil just until it begins to smoke, about 4 to 5 minutes. Add the batter to the skillet, the mixture will begin to sizzle right away. Remove the skillet immediately and sprinkle the top of the batter evenly with the remaining 1/2 cup each Cheddar and Monterey Jack.
Bake until a knife inserted into the middle of the cornbread comes out clean, about 30 minutes. Remove from oven and let stand for 10 minutes before cutting.
Recipe courtesy of Paul Prudhomme, author, "Louisiana Tastes"