Air fry the hatch chilies for 10-15 minutes at 375ºF or roast in the oven at 400ºF. Rotate the peppers half-way through. The peppers should be nicely blistered and evenly roasted. After about 12 minutes, remove the hatch chilis from the air fryer or oven and transfer them into a large bowl with a cover. Sprinkle with a pinch of salt, cover the bowl, and shake it up to disperse the salt. Let sit for at least five minutes.
After 5 minutes, remove the stems from the peppers and carefully peel the outside layer of the peppers off. Slice the pepper down the middle and gently scrape out all of the seeds using the back of your knife.
Cut the peppers into strips and dice them. Set aside in a bowl.
Roll the ground beef into 4 densely-packed meatballs. Remove any excess air in the meatballs by smacking it back and forth between the palms of your hands.
Heat up your griddle to the highest setting or a cast iron pan on medium-high heat.
Place about one and a half tablespoons of butter onto the griddle and toast your buns on one side until golden brown.
Place your meatballs onto the griddle. Take a square piece of parchment paper and place on top of each meatball and smash the burger down with a small heavy bottom pot. Smash the meat down hard enough so that the meat spreads wider than the bun.
Generously season each burger with salt and freshly ground pepper to taste. Then top each burger with sliced onions. Place any extra onions on the griddle and sauté with butter.
Use the parchment paper and pot again to flatten the onions on top of each of the burgers.
After about 4 minutes total cooking time on or until a nice crust forms on the bottom side of the burger, flip each patty over. At the time, add the hatch chilies to each of the burgers and top with a slice of cheese. Cover the patties with a large bowl to help melt the cheese faster if necessary. Once the onions are nicely caramelized and the cheese is melted, transfer the burgers onto the buns.
To build the burgers, top each of the patties with sliced pickles and spread a thin layer of yellow mustard on the top bun.
Serve with fries and enjoy!