Preheat the oven to 425°F. Grease an 8 or 9-inch square pan or casserole dish. Combine the flour, cornmeal, sugar, baking powder, and salt in a mixing bowl. Stir in the milk, oil, and egg just until moistened. Pour half of the batter into the prepared dish. Stir the browned hamburger into the chill beans. Pour this mixture over the layer of cornbread. Sprinkle with the shredded cheese to cover. Pour the remaining batter over the cheese layer and spread to cover. Bake for 25-30 minutes or until the sides are browned and a toothpick inserted in the center comes out mostly clean. Serve with remaining cheese and sour cream, if desired. Serves 6.