Preheat oven to 425 degrees. Place skillet in the preheating oven to warm up while you mix your batter.
In a large bowl, whisk together all of the dry ingredients - cornmeal, flour, sugar, baking powder, baking soda, and salt.
Add the buttermilk, melted butter, and eggs to the dry ingredients until just combined. Let the batter sit for 5 minutes in the bowl.
Remove the hot skillet from the oven and coat the bottom and sides with butter (you can also use a cooking spray or oil, but butter will provide the best flavor).
Pour your batter into the hot skillet and place back in the oven. Bake for 18-20 minutes, or until toothpick inserted into center comes out clean or with a few crumbs. Edges should be browned and top should have a light brown color. Allow cool for 10 minutes before serving.
Optionally, brush the top with more melted butter before serving.
If you do not have a cast iron skillet, this can me made in a 9 inch round pie pan. Baking time may need to be adjusted.