Arrange the drained onions in four distinct heaps on a baking sheet with a rim. Form the ground meat into four balls and compact them lightly. To make sure the onions stick to the beef, put the meatballs on top of the onion mounds and push down with your palm. Four inches is the ideal diameter for the finished patties. Rub the meat with a good amount of salt and pepper.
Heat the vegetable oil and butter in a 12-inch skillet over medium heat until the butter is melted. Carefully place the patties, onion side down, in the skillet using a big spatula. After 6 to 8 minutes of cooking, the onions should be a deep golden brown and beginning to crisp at the edges. Grill the burgers for another two minutes, or until browned all over, after flipping them. Turn the heat up to high.
Melt one or two slices of American cheese and top each burger. In the meanwhile, cover the buns with mayonnaise, mustard, and pickles. Put a burger on each of the bottom buns when the cheese has melted. Serve right away.
