Preheat the oven to 375 degrees F. Spray a 10-inch cast-iron skillet with oil and set aside. Sift together the flour, cornmeal, baking powder, salt and baking soda into a medium bowl. In a smaller bowl, whisk together the buttermilk, sugar, egg and oil. Put the prepared skillet over medium heat, add the butter, and heat until the butter melts and is just starting to sizzle. Tilt the pan to coat the sides and bottom. Pour the wet ingredients into the dry and combine them quickly, using as few strokes as possible. Scrape the batter into the prepared pan and bake the cornbread until it is golden brown, about 20 minutes. Let cool for a few moments, and slice into wedges to serve.