Heat a cast-iron skillet or griddle pan over medium-high. Form the beef into 4 thin patties. Season with salt and pepper. Press 1/4 cup onion into one side of each patty.
Place the patties, onion side down, in the skillet. Cook, pressing down with a spatula, until browned, 2 to 3 minutes per side. After you flip the patties, top with the cheese.
Butter the toast. Transfer each patty to a piece of toast. Top with the pickles, Dijon and remaining toast. Serve with the lettuce, tomatoes and onions.
