Step 1In a medium bowl, stir together the mayonnaise, ketchup, mustard, sweet and dill pickle relishes, Worcestershire sauce, vinegar, salt and sugar. This makes about ¾ cup sauce. The sauce will keep, covered and refrigerated, for up to two weeks.
Step 1Measure out 16 (2-ounce) patties of meat and flatten each patty to a thickness of approximately 1/4 inch. Season each side of the patty with a pinch of salt and set aside while you heat the griddle.
Step 2Toast the buns, cut-side down, on the griddle just until the cut sides begin to toast, about 30 seconds. Remove from heat and set aside.
Step 3Heat a griddle pan over medium heat until hot. Cook the burgers on one side until the patties start to brown, 45 seconds to 1 minute. Flip the burgers, adding a slice of cheese to the browned tops of each one. Continue to cook until the burgers are cooked and the cheese is beginning to melt, about 1 minute more. Remove from heat.
Step 4To assemble the burgers, slather about 1 tablespoon sauce on the toasted top and bottom of each bun. On the bottom of each bun, layer two lettuce leaves, a slice of tomato, one cheeseburger patty, a few onion rings, another cheeseburger patty and the top burger bun. Repeat with the remaining ingredients to form eight burgers. Serve immediately.