Peel the onions and slice them into very thin strands.
Divide the ground beef into 4 equal portions and gently shape into loose balls.
Heat a cast-iron skillet or griddle over medium-high heat.
Butter and toast the hamburger buns until lightly golden. Set aside.
Place the beef balls onto the hot skillet.
Immediately pile a generous portion of sliced onions over each beef ball.
Smash the onions and beef together into thin patties approximately ¼ inch thick.
Season with salt and black pepper.
Cook for 2–3 minutes, until the bottoms are deeply browned.
Scrape underneath the patties and flip so the onions are against the skillet.
Cook for another 2–3 minutes, until the onions are tender and golden and the beef reaches 160°F internally.
Add the American cheese and let it melt.
Transfer the burgers to the toasted buns.
Add dill pickles and mustard if desired.
Serve immediately.