For this, you need a griddle or flat top grill to set on your grill grates.
Heat the grill to 450 degrees F.
Form meat balls, about 4 ounces each. Season with salt and pepper and set aside.
Combine the mayonnaise and relish in a bowl and stir. Cover and refrigerate until the burgers are done.
Add half the butter to the flat top grill. Set the onion slices on the butter and grill until the onions soften, about 5 minutes. If you have room, you can toast the buns on the grill as well. Place the rest of the butter down and rub the buns in some butter, then allow them to toast.
Make sure the grill is dry where you’ll add the burgers. Place the meatballs on the grill. Wait a minute so the fat can loosen. Smash each ball to ½” thick with a spatula. Use a kitchen towel to place more pressure on the spatula to flatten the burgers, if necessary. Cook without touching for 2 minutes, until crispy edges begin to form. Scrape the spatula under the burgers to flip them, keeping the crispy edges intact. Immediately add a slice of cheese to each patty and cook without moving for 2 minutes, until the cheese is melted.
To assemble the burgers, remove the buns from the grill, slather on the mayonnaise, top with a patty, and onions.