Preheat the oven to 375° F.

Heat 2 tablespoons of the olive oil in a medium skillet. Add the onions, garlic, bell pepper, and jalapeño and sauté about 4 minutes, or until the vegetables are beginning to soften. Add the corn and sauté for several minutes. Remove the pan from the heat and set aside.

Sift the flour, cornmeal, baking powder, and salt together into a large mixing bowl and set aside. Mix the buttermilk with 2 remaining tablespoons of the olive oil and the eggs. Add the liquid to the dry ingredients and stir briefly to combine. Add the sautéed corn mixture and the cheeses and stir again to combine.

Heat a 10-inch round cast-iron skillet over a low flame and pour in the remaining 1 tablespoon of olive oil. Swirl the skillet around so that the olive oil completely coats all parts of the pan, bottom and sides. If a cast-iron skillet is not available, oil a square (8 x 8 x 2 inch) or rectangular (11 x 7 inch) glass baking dish well with the olive oil. Pour in the corn bread batter.

Place in the oven and bake for 40 minutes to 1 hour, or until a toothpick inserted into middle comes out clean and top is golden brown. (The cornbread in a glass baking dish will bake more quickly than in a cast-iron skillet, so begin checking after 40 minutes.) Remove the corn bread and let cool slightly in the pan on a rack before cutting and serving.

To serve, cut into wedges or squares.