Preheat oven to 375˚ F (or 380˚ F for HAB). Butter a loaf pan.
Whisk the cornmeal, flour, baking soda, and salt in a medium bowl.
Melt the butter in the microwave oven in a microwave - safe dish. Pour it into a medium bowl, and whisk in the sugar. When the sugar is incorporated, add the eggs and buttermilk, and continue to whisk until well blended. Stir in the cornmeal mixture, until well blended. There will be some lumps, but that's fine. Pour batter into the prepared loaf pan.
Bake for 30 to 40 minutes, or until a toothpick inserted in the center comes out clean. At sea level, the time will be closer to 30 minutes, but baking at high altitude will take closer to 40 minutes. Cover with foil in the last 10 minutes of baking - this will help to keep the cornbread moist, and help it to bake more evenly.
Cool in the loaf pan for 10 minutes before removing. Run a sharp knife around the cornbread, separating it from the sides of the pan. Flip out onto a cutting board for easy slicing.