Preheat your oven to 400°F (200°C) and grease an 8-inch square baking pan or cast-iron skillet with butter.
In a large bowl, whisk together cornmeal, flour, sugar (if using), baking powder, and salt.
In another bowl, beat the eggs, then stir in the milk and melted butter until combined.
Pour the wet ingredients into the dry ingredients and stir gently until just combined. The batter should be thick but pourable.
Pour the batter into the prepared pan and smooth the top with a spatula.
Bake for 20–25 minutes, or until a toothpick inserted into the center comes out clean. The top should be lightly golden brown.
Let cool for 5 minutes, then slice into 8 pieces and serve warm.