Roast the hatch chiles over an open flame or on a hot skillet, turning occasionally until the skin is charred and blistered, about 8-10 minutes. Cover and steam for 5 minutes, then peel and chop.

In a large mixing bowl, combine ground beef, chopped hatch chiles, and pimento cheese. Season with salt and pepper; mix thoroughly.

Divide the mixture into equal portions and shape into patties, slightly larger than the buns. Refrigerate for 10 minutes.

Preheat the grill to medium-high heat (400°F). Grill the patties for 6-7 minutes per side until cooked to desired doneness (medium is 160°F).

Remove cooked patties and let rest. Toast burger buns on the grill for 1-2 minutes, then assemble with patties, lettuce, tomato, and extra pimento cheese.