Preheat oven to 375 degrees F.
Grease a 9-inch square baking dish with 1/2 tablespoon butter.
Combine eggs, buttermilk, and 4 tablespoons melted butter in a large mixing bowl, and whisk to combine. Combine cornmeal, flour, baking powder, sugar, salt, and baking soda in a separate large bowl, and whisk to combine. Add wet ingredients to dry ingredients and stir until just combined. Pour batter into prepared baking dish. Bake until top is golden brown and edges have pulled away from sides of pan, about 30 minutes. Remove from oven and let stand for 5 minutes.
Yield: 1 (9-inch) square; 8 cups crumbled