Preheat the oven or toaster oven to 200C while you cook the onions
Form ground beef into eight 60g patties, using damp hands (or a plate) to press each into a patty about 5mm thick and 10cm wide. Season generously with salt and pepper
Heat 2 tsp oil in a non-stick skillet over medium-high heat until shimmering.
Add onions and 1 tsp salt to skillet. Reduce heat to medium low, and cook, tossing and stirring occasionally until onions are well browned, about 15 minutes.
Once onions begin to sizzle heavily and appear dry, add 1 tablespoon water to skillet and stir.
Continue cooking until water evaporates and onions start sizzling again.
Repeat process, adding 1 tablespoon of water with each iteration until onions are meltingly soft and dark brown, about 3 times total. Transfer to a small bowl and set aside.
Combine mayonnaise, ketchup, relish, sugar, and vinegar in small bowl. Stir to combine.
Place closed buns in preheated oven for 2 minutes until slightly darkened and crisped. Heat 1/2 tsp oil in non-stick skillet or griddle over medium-high heat until shimmering.
Open buns and add face-down to skillet. Toast until dark brown around the edges, about 1 minute total.
Add remaining 1/2 tsp oil to pan, swirl to coat, and heat over medium-high heat until lightly smoking. Add burger patties and cook without moving until well browned and crusty on first side, about 2 1/2 minutes
While they are cooking, spread 1 tablespoon mustard on raw side of each patty with a spoon
Top each bottom bun with spread, 4 slices pickles, 1 slice tomato, and lettuce.
Flip patties with a thin spatula so mustard side is down and continue to cook for 1 minute. Top each patty with a slice of cheese. Divide onion mixture evenly between half of the patties. Place the other patties directly on top of the onions, sandwiching them between the beef.
Transfer patty stacks to bottom bun. Top with top bun, and serve immediately.