Optional toppings: Lettuce leaves and sliced tomato
Grill peppers, covered, over high heat until all sides are blistered and blackened, 8-10 minutes, turning as needed. Immediately place peppers in a small bowl; let stand, covered, 20 minutes. Reduce grill temperature to medium heat.
Meanwhile, in a large bowl, combine beef, salt and pepper; mix lightly but thoroughly. Shape into six 3/4-in.-thick patties.
Peel off and discard charred skin from peppers. Cut peppers lengthwise in half; carefully remove stems and seeds. Cut into slices or coarsely chop.
Grill burgers, covered, over medium heat until a thermometer reads 160°, 5-7 minutes on each side. Top with cheese and chiles; grill, covered, until cheese is melted, 1-2 minutes longer. Top bun bottoms with burgers and, if desired, lettuce and tomato.