Preheat oven to 375 degrees. Grease an 8 inch square pan.

Melt butter and add to a mixing bowl. Stir in sugars until well combined. Add eggs and stir well.

Combine buttermilk with baking soda and stir into the bowl.

Add cornmeal, flour, and salt and stir until combined. Avoid over-mixing--the batter doesn't need to be completely smooth.

Pour batter into the prepared pan. Bake at 375 degrees F for 22-30 minutes, or until a toothpick inserted in the center comes out clean.