Combine the onion slices and 1 teaspoon of salt in a bowl and toss to combine. Transfer the onions to a colander and let sit for 30 minutes, tossing occasionally. Transfer the onions to a clean dish towel, gather the edges together and squeeze out as much liquid as you can from the onions. Do this over the sink or a large bowl since the onions will have quite a bit of liquid in them.
Divide the onions into 4 separate mounds on a rimmed baking sheet. Form the beef into 4 lightly packed balls. Place the beef balls on top of the onion mounds and flatten the beef firmly (use your palm) so the onion adheres to the beef. The patties should measure 4 inches in diameter. Season the beef generously with salt and pepper.
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