Put a 10-inch cast iron skillet in the oven and heat it for at least 30 minutes. Meanwhile, prepare the batter.
Whisk together the flour, cornmeal, sugar, baking powder and salt in a large bowl. In a medium bowl, whisk together the milk, eggs and melted butter.
Make a well in the center of the dry ingredients and pour the wet mixture into the well. Use a fork or spatula to stir the batter until evenly combined.
Remove the hot skillet from the oven, add the fat and swirl to coat the bottom. Pour the batter into the skillet and, using a spatula, spread the batter evenly across the pan. Bake until lightly golden brown, firm and springy to the touch, about 25 to 30 minutes (see Cook's Note). Remove from the oven and serve directly from the skillet, if desired.
For a richer flavor, you can melt an additional 2 tablespoons butter over the top of the cornbread when it comes out of the oven.