Preheat oven to 425 degrees F. Grease the bottom and sides of a cast iron skillet with softened butter.
In a mixing bowl, whisk together cornmeal, flour, sugar, baking powder, baking soda, and salt. In another bowl, whisk together the buttermilk, eggs, and melted butter until even.
Pour the liquid into the dry ingredients and use a whisk to combine until smooth. Transfer to the greased skillet.
Bake for 25-30 minutes or until firm to the touch, golden brown, and a toothpick inserted into the center comes out clean.