Preheat the oven to 375 degrees F (175 degrees C). Grease an 8-inch square pan.

Melt butter in a large skillet over medium heat. Remove from heat and stir in sugar. Quickly whisk in eggs.

Combine buttermilk and baking soda in a small bowl; whisk mixture into the skillet. Stir in cornmeal, flour, and salt until well-blended and only a few lumps remain. Pour batter into the prepared pan.

Bake in the preheated oven until a toothpick inserted in the center comes out clean, 30 to 40 minutes.