Preheat the oven to 425 degrees . In a 9-inch cast-iron or other heavy ovenproof skillet, melt the butter over medium-low heat.
Meanwhile, in a large bowl, whisk together the cornmeal, flour, sugar, baking soda, 1/2 tsp. salt and 1/4 tsp. pepper. In a medium bowl, whisk together the buttermilk and eggs and stir into the dry mixture.
Swirl the butter around the skillet to coat the inside, then pour into the dry mixture. Stir just until moistened, then pour the batter into the skillet. Bake until golden, 20 to 25 minutes.