Create your campfire coal bed. For this, you need a griddle or flat top grill to set on your grill grates.
Roll the meat into 8-ounce balls. Before setting aside, season with salt and pepper.
In a bowl, mix together the relish and mayonnaise. Keep covered and chilled until burgers are cooked through.
Spread half of the butter out on the grill's flat top. Grill the onion slices for approximately 5 minutes, or until they begin to soften, while spread them out on the butter. If there's enough room, you may also toast the buns on the grill. Toast the buns after laying the remaining butter on the bottom and rubbing them with butter.
Prior to adding the burgers, ensure that the grill surface is completely dry. Before grilling, arrange the meatballs. Let the fat soften for a moment. To make each ball ½" thick, use a burger press or spatula to smash them. Keep moving the burgers around every 2 minutes or until the edges start to get crispy. Flip the burgers over by scraping the spatula under them, being careful not to break off any of the crispy ends. Quickly top each burger with a slice of cheese and cook, undisturbed, for 2 minutes, or until the cheese melts.
Burgers are ready when the buns are taken off the grill. Spread mayonnaise on the buns, then place a patty on top. Finally, add onions.