Preheat the oven to 375 degrees F (175 degrees C). Grease an 8-inch square pan.
Melt butter in a medium sized microwaveable bowl. Add in sugar and mix well. Whisk in the eggs quickly.
Combine buttermilk and baking soda in a small bowl; whisk this mixture into the butter and egg mixture. Stir in the cornmeal flour and salt until well blended and only a few small lumps remain. Pour it into the prepared baking pan.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, 30 to 40 minutes.