Roast and peel the Hatch chiles: char the skins over a gas flame or under a broiler, then steam in a bowl covered with plastic wrap for 10 minutes. Peel off the blackened skin, cut off the stems, and slit each chile open to remove the seeds. Set aside.

Preheat the oven to 375°F. In a large skillet, heat the olive oil over medium heat. Add the sliced red onion and garlic, and cook until soft and lightly browned, about 7 minutes. Stir in the corn and smoked paprika, and cook for another 2 minutes to blend flavors. Remove from heat and set aside.

In a large mixing bowl, whisk together the cornmeal, baking soda, sugar, and salt. Make a well in the center, then add the buttermilk and eggs. Stir until the batter is smooth. Fold in the melted butter and the cooked onion-corn mixture.

Lightly oil a 9×13-inch baking dish. Place 6 of the prepared chiles, smooth side down, in a single layer in the dish. Pour about 2 cups of the batter evenly over the chiles. Sprinkle with 3/4 cup of the grated cheddar. Arrange the remaining 6 chiles, smooth side down, on top of the cheese. Pour the remaining batter (about 2 1/2 cups) over the top, and sprinkle with the remaining 1 1/4 cups of cheese.

Bake in the preheated oven until the top is golden brown and the batter is set, about 25 minutes. If the top isn't brown enough, broil for 30 seconds. Let the casserole cool in the pan for at least 20 minutes before slicing and serving.