Preheat the oven to 400°F (200°C)
Grease an 8-inch square baking pan or cast-iron skillet
In a large bowl, mix 1 cup cornmeal, 1 cup all-purpose flour, 1/4 cup sugar, 1 tablespoon baking powder, and 1/2 teaspoon salt
In another bowl, whisk 1 cup milk, 2 eggs, and 1/4 cup melted butter
Pour the wet ingredients into the dry ingredients
Stir until just combined
Fold in 1/2 cup corn kernels if desired
Pour the batter into the prepared pan
Bake for 20 to 25 minutes, until golden and a toothpick comes out clean
Let cool slightly before slicing and serving