Preheat oven to 400 degrees F (205 degrees C). Lightly grease an 8-inch square baking dish.
Combine flour, cornmeal, sugar, baking powder, baking soda, and salt in a large bowl. Mix egg, sour cream, milk, and butter in a small bowl. Fold egg mixture into flour mixture until just moistened; pour into prepared baking dish.
Bake in preheated oven until a toothpick inserted near the center comes out clean, 20 to 25 minutes. Serve warm.