Combine the onion slices and 1 teaspoon salt in a bowl and stir to combine. Transfer the onions to a colander and leave for 30 minutes, stirring occasionally. Transfer the onion to a clean kitchen towel, bring the ends together and squeeze as much liquid from the onion as you can. Do this over a sink or large bowl because the onions will retain a little more liquid.
Divide the onions into 4 separate piles on a rimmed baking sheet. Shape the meat into 4 loosely packed balls. Place the beef strips on the piles of onions and spread the meat vigorously (use the palm of your hand) so that the onions stick to the beef. The pancakes should be 4 inches in diameter. Generously season the beef with salt and pepper.
Melt the butter with the oil in a 12-inch skillet over medium heat. Using a large spatula, transfer the patties to the skillet, onion side down. Cook for 6-8 minutes, until the onions are a deep golden brown and beginning to crisp around the edges. Flip the burgers, then increase the heat to high and cook until nicely browned on the second side, about 2 minutes.
Add one or two slices of cheese to each burger and let it melt. Add mayonnaise, mustard, and pickle to the top bun, then place each burger on the bottom bun. Serve immediately.
Enjoy !
