Grease a 9-by-13-by-2-inch baking pan with butter. Heat the oven to 425 F.
Combine the cornmeal, flour, salt, baking powder, and soda in a large bowl. In another bowl, whisk eggs with buttermilk; add to the dry mixture along with melted butter. Mix until blended.
Spread the batter in the prepared pan and bake for 15 to 20 minutes, until browned around the edges.