1 ½ pounds ground round
1 (4.5-ounce) can chopped green chiles, drained
1 tablespoon chili powder
½ teaspoon kosher salt
½ cup mayonnaise
1 tablespoon fresh lime juice
2 teaspoons ground cumin
2 tablespoons olive oil, divided
6 (3/4-ounce) Monterey Jack cheese slices
6 sesame seed hamburger buns, toasted
1 cup loosely packed fresh cilantro leaves
Heat a camping stove or grill to medium high (375° to 400°F), or fit a grilling grate over the direct heat of glowing embers. Gently combine the beef, chiles, chili powder, and salt in a medium bowl. Gently shape the mixture into 6 (4-inch) patties. Stir together the mayonnaise, lime juice, and cumin in a small bowl; set aside.
Heat 1 tablespoon of the oil in a 12-inch cast-iron skillet on the camping stove or grilling grate directly over the heat source. Add 3 patties; cook, covered, until the beef is no longer pink in the center, 4 to 5 minutes per side. Top each patty with 1 cheese slice; remove to a plate, and loosely cover with heavy-duty aluminum foil. Repeat with the remaining 1 tablespoon oil and 3 patties.
Spread the mayonnaise mixture evenly on the cut sides of the toasted buns. Top the bottom halves of the buns with the patties, cilantro, and the top halves of the buns.