In a small bowl, cover onion with cold water; set aside until ready to use.
Form beef into 8 patties about 1" wider than buns; season all over with salt and pepper.
In a large heavy skillet over medium-high heat, heat oil. Working in batches, cook buns cut side down, adding more oil if needed and watching closely, until lightly browned, about 1 minute. Transfer buns to a cutting board.
In same skillet over medium-high heat, cook 4 patties, flipping halfway through, until well browned, 1 to 2 minutes per side. Transfer to a plate. Repeat with remaining patties.
Drain reserved onions and spread on a paper towel-lined plate. Spread some sauce across bottom bun. Top with a slice of cheese, some onions, lettuce, 3 pickles, and a burger patty. Top with a second bottom bun, more sauce, onions, lettuce, and 3 pickles. Top with a second burger patty. Close with top bun. Repeat to make 3 more burgers.
