Preheat oven to 350°F/175°C. Grease an 8x8 or 9x9 baking dish or pan.
In a large bowl, cream together the butter and sugar. Mix in the eggs and salt, then add the buttermilk and mix. Add the cornmeal, flour, baking powder, and baking soda and mix until combined.
Pour batter into the prepared baking dish. Bake for 25-35 minutes, until golden brown around the edges and a toothpick inserted into the center comes out clean. (An 8x8 size may take longer to cook because the cornbread will be thicker than in a 9x9 pan.)
Serve warm with butter and honey, honey butter, soup, stew, chili, etc.
Double the recipe for a 9x13 size pan. Buttermilk Substitution: 1 cup milk + 1 tablespoon lemon juice or white vinegar. Stir together and let sit for 5 minutes before adding to the batter.