Place the onion slices in a large bowl.
Toss with 1 teaspoon of salt and let rest for 30 minutes to extract as much liquid out of the onions as possible.
Transfer the onions to a towel or a few sheets of paper towels, roll up tightly and squeeze to remove as much liquid as you can.
Divide the onion slices into 4 equal piles on a cutting board or flat surface.
Divide the beef into 4 patties and form into balls.
Place beef on top of the onions and, using the palm of your hand or the bottom of a small skillet, flatten the beef into patties. The onions will stick to the bottom of the patties. That's what you want.
Season patties with salt and pepper.
Heat up a griddle or cast iron skillet on your stove top or grill over medium-high heat.
Add the butter and swirl it around to coat the griddle or skillet.
Add the patties, onion side down, and cook for 6-8 minutes. You'll see the onions starting to turn golden brown and get crispy around the sides.
Flip and continue cooking until the burgers are done, about 2 more minutes.
Top with cheese and remove.
Toast the buns, if desired.
Add the patties, mayonnaise, mustard, and pickles.