Preheat the oven to 325°F.
In a large mixing bowl, whisk together the all-purpose flour, cornmeal, sugar, baking powder, and salt.
In a separate bowl, whisk together the eggs, buttermilk or milk, and oil.
Pour the egg mixture into the flour mixture; stir to combine.
Place the butter in a very deep 10-inch cast iron skillet (at least 2 inches in depth), or in a very deep 9-inch square baking dish. If you don’t have a skillet or deep dish this size, you can use another similar 2-3 quart dish, such as an 11 x 7-inch pan. If using a smaller 8-inch square pan, don’t fill it to the top with all of the batter (or it might overflow in the oven). Bake the extra batter in muffin tins, if necessary.
Put the skillet in the oven for about 3-5 minutes, until the butter melts. Use a pastry brush to coat the inside of the skillet with the melted butter.
Transfer the batter to the buttered skillet.
Bake for 40-45 minutes, until a toothpick inserted in the center comes out clean. Let cool for 15 minutes before cutting into squares or wedges and serving.