Preheat the oven to 375 degrees F.
Combine the cornmeal, flour, sugar, and salt in a bowl.
Combine the buttermilk and the baking soda. Make a well in the dry ingredients, and add the buttermilk. Whisk in.
Beat the eggs, then add them to the mixture.
Melt the butter in a cast-iron skillet in the oven. When melted, pour most of the butter into the batter, leaving just a little bit to coat all of the edges of the pan. Working quickly, whisk the butter into the batter, and then pour it into the cast-iron skillet.
Bake for 35 to 40 minutes, until a toothpick inserted into the center comes out clean.