Preheat the oven to 425°F.
Lightly grease an 8-inch baking dish or cast iron skillet.
In a large mixing bowl, whisk together the cornmeal, flour, sugar, baking powder, baking soda, and salt.
Add the eggs, buttermilk, and melted butter.
Stir until just combined. A few lumps are perfectly fine.
Pour the batter into the prepared baking dish.
Bake for 20 to 25 minutes, or until the top is golden and a toothpick inserted into the center comes out clean.
Let cool for 10 minutes before serving.