Preheat oven to 425. Butter an 8 inch square baking dish. Whisk together cornmeal, salt, sugar, and baking powder in a large bowl. Whisk together eggs, buttermilk, and butter in a medium bowl. Add egg mixture to cornmeal mixture, stir to combine.
Pour batter into prepared baking dish. Bake until golden and toothpick inserted into center comes out clean, about 25 minutes. Let cool slightly in dish on wire rack. Run knife around edges of dish to loosen, and invert onto rack to cool completely. Cornbread can be wrapped in plastic and stored at room temperature for up to 3 days. For dressing, let stand overnight, uncovered, to dry out before crumbling.