Preheat the oven to 425˚F (220˚C). Place a 10-inch cast-iron skillet in the oven for 10 minutes to heat up.
In the meantime, in a large bowl, whisk together the cornmeal, flour, baking powder, baking soda, salt and sugar. Make a well in the center of the bowl, and crack in the eggs. Stir the eggs gently to break them up. Add the buttermilk and stir until mostly incorporated. Pour in the butter and fold until just combined.
Take the skillet out of the oven (be careful—it’s hot!), and add the vegetable oil. Swirl to coat. Pour the batter into the hot skillet and smooth out the top. Bake the cornbread until the top is golden brown and lightly cracked (a toothpick inserted in the center should come out clean), about 15-18 minutes. Let the bread cool in the skillet on a wire rack for at least 10 minutes before serving.
