Divide ground beef into 10 equal pieces, about 1/5lb per piece. Keep chilled until ready to grill.
Heat cast iron griddle to 450° or as hot as you can get it. Meanwhile, make the Special Sauce by whisking together the mayo, mustard, ketchup, salt and pepper until well combined. Set aside.
Brush the hot griddle with the cooking oil. Working in batches, place two patties at a time (or more if your griddle is large) on the griddle and use a spatula to firmly press them down until very flat. Sprinkle with a mix of salt and pepper. Cook for 1-2 minutes then flip to the other side. Cook 1-2 minutes more. Place a slice of cheese on each patty and close grill lid or cover and let melt. Continue until all patties are cooked.
Toast buns and schmear with Special Sauce. Add two patties to each bun then top with diced onions and top bun. Enjoy immediately!