Preheat the oven to 425º. Lightly grease an 8-inch baking dish.
In a large bowl, mix together the cornmeal, flour, baking soda and salt.
In a separate bowl, whisk together the eggs, buttermilk, and melted butter. Add the wet ingredients to the cornmeal mixture and gently fold just until no dry pockets remain—the batter should still be slightly lumpy. Pour the batter into the prepared baking dish.
Bake until the top is golden brown and a toothpick inserted into the center comes out clean, about 20–25 minutes. Remove from the oven and let the cornbread cool for 10 minutes before slicing and serving.