Gently combine beef, grated onion and Worcestershire in a large bowl. Shape into 8 patties as thin as possible (about 5 inches in diameter) and place on a cookie sheet lined with plastic wrap. Cover and refrigerate for 30 minutes to combine flavors.
Heat gas or charcoal grill to medium-hot. Using a long-handled brush, season rack with vegetable oil.
Season patties with salt and pepper and grill, covered, 2 minutes. Turn and grill, covered, for 1 minute. Place a cheese triangle on each patty and grill for 1 minute longer, or until patties register 160 degrees F on an instant-read thermometer.
Place the bottom halves of the warm rolls on a serving plate. Stack each with a lettuce leaf, tomato slice, 1 teaspoon of dressing, a burger with cheese, a pickle slice and an onion slice. Stack a second layer on top of the first, starting with the lettuce and ending with the pickle. Add the top halves of the rolls and serve warm. Makes 4 servings.