Preheat the oven to 425 degrees F and position a rack in the middle. Butter an 8-inch-square baking pan.
Melt the butter in the microwave in a microwave-safe dish in three 15-second intervals on high or in a small pan on the stove. Set it aside to cool.
In a bowl, whisk together the flour, cornmeal, baking powder, baking soda and salt.
In a large bowl, whisk together the buttermilk and the eggs. Add the melted butter. Add the flour-cornmeal mixture and stir just until combined. Pour the batter into the pan. Bake until the cornbread just begins to brown and a toothpick inserted in the center comes out clean, 18 to 23 minutes. Cool for about 10 minutes before serving.
Photographs by Yunhee Kim
Recipe courtesy Cat Cora for Food Network Magazine