Make the burger patties by rolling ground beef into balls that are about 3 - 3.5 oz each, or a bit larger than the size of a golf ball.
Press each burger ball down until you have an even, thin patty. The patty should be slightly thicker than a smash burger patty.
Tear each slice of American cheese into about 4 squares. Pile the torn squares of 2 slices of cheese in the middle of one burger patty. Leave about 1/2" from the edge of the cheese to the edge of the beef patty. Place a second burger patty on top so that the cheese is in the middle of the two patties.
Use your fingers to seal the burger patty together on all sides. Be sure that the patty is completely sealed so the cheese doesn't ooze out when cooking.
Start cooking sliced onions on the heated griddle.
When the onions are almost done cooking, add the cheese stuffed burger patty to the griddle. Season the top of the patty with salt and pepper or your favorite burger seasoning. Allow it to cook on the first side without touching it.
When the burger is about 3/4 cooked through, flip it to the second side. Season the other side (now top side) of the burger. Continue to cook the burger until done.
When burger is almost done cooking, dab the cut side of your hamburger buns in the leftover grease on the griddle. Then toast them on the griddle.
When onions and burgers are done cooking, build your Juicy Lucy cheese stuffed burgers and serve warm with your favorite burger toppings.