Pre-heat oven to 400 degrees. Butter an 8X8 metal baking dish.
Mix the flour, cornmeal, baking soda, baking powder, sugar, and salt in a large bowl. In a separate small bowl whisk together the buttermilk, butter, and eggs.
Add the milk mixture to the dry ingredients, add the cheese and then mix until just it's all incorporated - don't over mix.
Pour into greased baking dish and bake until top begins to golden and tester comes out cleanly.
Cool a little in pan or on rack and serve warm.
Store in an airtight container or foil at room temperature.