Heat a large pan or griddle over medium high heat. Add the Hatch chiles and onion, season with kosher salt and cook until the onions are soft about 10 minutes. Remove from the pan and set aside. Coat each burger bun side with mayo and lightly toast the buns on the hot pan until golden, about 2 minutes.
Divide the beef into four equal parts and roll them into meatballs. Season with Salt Pepper + Three Chiles.
Lightly oil the pan and place the burgers on the pan. Once juices start to pool at the bottom of the burger use a smash burger press or large metal spatula to smash the burger until it is SUPER THIN! Once you see juices pooling on the meat flip the burger. Spoon some of the chiles and peppers onto each burger patty and add the cheese. Cover the burgers and cook for just 1 minute more or until the cheese is melted.
Build the burgers with layer of lettuce on each bun, one burger patty with all its Hatch chiles goodness and another bun for topping.