Preheat the oven to 400ºF. Grease an 8 or 9 inch square baking dish.
In a large bowl, combine flour, cornmeal, sugar, baking powder, and salt. Add milk, oil, and egg and stir until just moistened. Fold in cheese. Pour the batter into the prepared pan and bake for 25-30 minutes or until lightly golden and a toothpick inserted in the center comes out clean.