Preheat oven to 425 degrees. Brush bottom and sides of a 13-by-9-inch baking pan with 2 tablespoons butter.
In a medium bowl, whisk together cornmeal, flour, sugar, baking soda, and salt; set aside. In a large bowl, whisk together eggs and buttermilk; whisk in remaining butter. Stir cornmeal mixture into buttermilk mixture just until moistened. (Do not overmix.)
Pour batter into prepared pan, and bake until golden and a toothpick inserted in center comes out clean, 15 to 20 minutes. Let cool in pan at least 15 minutes before inverting and slicing.