How to Make It
Using your hands, combine beef, onion, chiles, salt, and black pepper in a large bowl just until evenly incorporated. Shape into 8 (2 1/2-ounce) balls.
Heat a large cast-iron skillet or griddle over high until smoking. Add 2 tablespoons oil. Add 4 meatballs, and immediately flatten to 1/4-inch-thickness with a sturdy, wide spatula. Cook until bottoms are crisp and deep brown, about 1 minute. Flip patties, top each with 1 cheese slice, and cook until bottoms are well charred and cheese is melted, 45 seconds to 1 minute. Remove from skillet, and cover to keep warm. Repeat with remaining 2 tablespoons oil, remaining 4 meatballs, and remaining 4 cheese slices.
Preheat broiler to high with oven rack 5 to 6 inches from heat. Brush cut sides of buns with butter. Arrange buns, cut side up, on a baking sheet. Broil in preheated oven until toasted, 1 to 2 minutes. Spread each bottom bun half with 1 1/2 tablespoons mayonnaise, top with 2 patties, and spoon 1 1/2 tablespoons Hatch chile salsa over top. Cover with top bun halves, and serve immediately.