Directions

1. Over a low gas flame or under the broiler, roast chile until charred, about 6 minutes, turning frequently. Place in a bowl and cover bowl tightly with plastic wrap. Let chile steam 20 minutes, then rub with a paper towel to remove skin. Remove stem and seeds. Slice chile into 2-inch strips and return to bowl.
2. In a large skillet, heat 2 teaspoons oil over medium-high. Add onion and season with salt and pepper. Cook until onion is soft and translucent, about 10 minutes. Add onion to bowl with chile and stir to combine.
3. Form ground chicken into four 4-inch-wide patties and season with salt and pepper. Heat a large nonstick skillet over medium-high. Add 2 teaspoons oil and swirl to coat. Working in batches, cook burgers 2 minutes. Flip, top each with cheese, and cook until cooked through, about 4 minutes more.
4. Meanwhile, heat broiler. Butter inside of buns and place on a baking sheet, buttered side up. Toast under broiler. Place burgers on buns and top with onion-and-chile mixture.