Divide the meat into 8 equal portions. Shape each portion into a thin patty that 's about 1 inch wider than the hamburger buns. Place 1 slice of cheese and 1 slice of onion on 4 of the patties. Place the remaining patties on top and seal the patties well concealing the cheese and onion. Transfer the patties to a plate and refrigerate.
Heat a grill pan or outdoor grill. When the grill is ready, use tongs to rub the grate with several layers of paper towels dipped in oil.
Season the hamburger patties well on both sides so that you can see a thin layer of salt and pepper. Place the patties on the grill , cover the grill, and cook until grill marks appear on the bottom, about 3 to 4 minutes. Using a spatula, turn over and cook for about 2 minutes more. Place 1 slice of cheese on 4 patties, cover the grill, and continue cooking, about 3 to 4 minutes more. Remove to a clean plate and tent loosely with foil.
Place the bun halves cut-side down on the grill and toast until golden brown, Remove the buns to a clean serving plate, mix equal parts thousand island dressing and mayonnaise together,spread on both sides of buns. Place a patty on each bun bottom, add lettuce and tomatoes and pickles,cover with a bun top.