Preheat the oven to 375°F (190°C) and grease a 9-inch square baking pan or cast-iron skillet.

In a large mixing bowl, cream together the butter and sugar until smooth and well combined.

Beat in the eggs one at a time, ensuring each is fully incorporated before adding the next.

Stir the buttermilk into the butter, sugar, and egg mixture.

In a separate bowl, whisk together the cornmeal, all-purpose flour, baking soda, and salt.

Gradually mix the dry ingredients into the wet ingredients, stirring until just combined. Be careful not to overmix the batter.

Pour the batter into the prepared pan, spreading it evenly.

Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.

Remove from the oven when the top is golden brown and the edges are slightly pulling away from the sides of the pan.

Let the cornbread cool in the pan for 10 minutes.

Cut into squares and serve warm, preferably with a pat of butter.