Preheat the oven to 400°F. Place a 9-inch cast-iron skillet in the oven to heat. In a bowl, combine the flour, cornmeal, baking powder, baking soda, and salt. Add the buttermilk, eggs, and melted butter and stir. Carefully remove the heated pan from the oven. Add the cold butter and let it sizzle until it browns and the noise subsides, then pour the batter into the pan. Return the pan to the oven and bake for 15 to 17 minutes, until the craggy ridges on top of the cornbread start turning brown. Serve warm.