In a medium bowl, stir together the cornmeal, flour, granulated sugar, baking powder, baking soda, and kosher salt. Whisk in the eggs, melted butter, and milk until a smooth dough forms. Gently fold in the shredded cheese, chopped jalapeño, chopped bell pepper, and minced green onion. Pour the batter into the prepared pan and smooth into an even layer with a spatula.
Bake 25 minutes, until puffed and a toothpick comes out clean. Allow to cool for a few minutes, then slice into pieces and serve.