Preheat the oven to 375°. Rub a 10-inch cast-iron skillet with oil; heat it in the oven.
In a bowl, whisk the cornmeal with the flour, sugar, baking powder, baking soda, salt and pepper. In another bowl, whisk the eggs, buttermilk, sour cream and butter, then whisk into the dry ingredients until combined. Pour the batter into the skillet.
Bake the corn bread for about 35 minutes, until risen and golden and a toothpick inserted in the center comes out with a few moist crumbs. Let cool for 20 minutes. Cut into wedges and serve.