To make caramelized onions: Place sliced onions in a microwave-safe bowl. Cook for about 8 minutes in microwave until onions are very soft. In a large nonstick pan, add olive oil and heat. Add cooked onions and 2 tablespoons of Worcestershire sauce. Sauté on medium-high heat until onions are browned, about 8 minutes. Stir often. Keep warm or reheat before serving.
Lightly oil grill and heat grill to medium.
In a large bowl, add ground beef, egg white, grated onions, 3 tablespoons Worcestershire sauce, seasoning salt, and pepper. Using your hands or a fork, gently mix together. Handle meat as little as possible–the more you work it, the tougher it gets.
Shape meat into 5 patties. Place burgers on grill, close lid, and cook until NO LONGER PINK INSIDE, turning once, about 5 minutes per side. If using an instant-read thermometer, it should read 160F. Try not to abuse your burgers by pressing with a spatula, pricking with a fork, or turning frequently as precious juices will be lost!
Line each plate with a large lettuce leaf. Top with a burger. Top each with tomato slices and caramelized onions. Let everyone dress their own. Serve with condiments such as thousand island dressing, ketchup, and mustard.