Homemade Buttermilk Cornbread

1/4 cup unsalted butter, melted, plus more, room temperature, for baking pan
1 cup yellow cornmeal
1 cup all-purpose flour (spooned and leveled)
1/4 cup sugar
1 1/2 teaspoons baking powder (for a fluffier cornbread, add 1/2 teaspoon baking soda)
1 1/2 teaspoons coarse salt
1 cup low-fat buttermilk
2 eggs

Preheat oven to 400 degrees. Butter a 9-inch square baking pan. In a large bowl, combine cornmeal, flour, sugar, baking powder, baking soda (if using), and salt. In a medium bowl, whisk together buttermilk, butter, and eggs (mixture might appear curdled). Add to flour mixture and stir just until combined (do not overmix). Transfer to baking pan and smooth top.
Bake until a toothpick inserted in center comes out clean, 20 to 25 minutes. Let cool on a wire rack 15 minutes before serving.