Preheat oven to 400°F (200°C). Grease a 9-inch cast iron skillet or 8x8 baking pan and place it in the oven while preheating.
In a large bowl, whisk together the cornmeal, flour, sugar, baking powder, and salt.
In a separate bowl, whisk together the buttermilk, melted butter, and eggs until combined.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix — a few lumps are fine.
Carefully remove the hot skillet from the oven. Pour the batter into the hot pan.
Bake for 20 to 25 minutes, until the top is golden brown and a toothpick inserted in the center comes out clean.
Let cool in the pan for 5 minutes before slicing and serving.