Cut dark-green tops off scallions, and finely chop. Preheat a large cast-iron skillet over medium-high heat. Place scallions, onion, and chiles in skillet, and cook, undisturbed, until charred on bottom, about 5 minutes. Turn vegetables with tongs, and cook, undisturbed, until charred on other side, about 5 minutes. (Vegetables can also be broiled on a baking sheet.)

Transfer scallions to a blender. Continue turning and charring chiles and onion until charred on all sides, 5 to 10 minutes more. Remove skillet from heat. Transfer onion to blender.

Transfer chiles to a bowl, cover immediately with plastic wrap, and let steam 15 minutes. Peel and discard charred skin from chiles, and remove stems and seeds. Halve chiles lengthwise, and slice crosswise into 1/4-inch-thick strips.

Add 2 1/2 cups corn, the salt, and 2 cups water to blender. Puree until smooth, about 1 minute. Transfer puree to skillet. Stir in remaining corn and 2 cups water. Bring to a boil over high heat, reduce heat, and simmer, stirring occasionally, until thickened slightly, about 8 minutes.

Whisk together cornmeal and remaining 3 tablespoons water. Stir into soup along with chiles, and simmer until it has the consistency of porridge, about 2 minutes.

Divide soup among 6 bowls; garnish with chopped scallion greens, and sprinkle with cheese. Soup can be refrigerated 2 days; let cool completely before refrigerating. Gently reheat in a covered pot over medium heat, stirring occasionally.