Heat the butter and EVOO in a skillet. Add in the onion and sprinkle with the sugar. Sauté the onion over medium low heat until they are golden and tender and gorgeous.
While the onions are doing their thing, prepare your burgers.
In a bowl combine the ground beef, onion powder, 2 tablespoons of Worcestershire sauce, and the salt & pepper. Mix the beef and then form it into 6 burgers.
Place these on your broiler pan and broil for about 5-6 minutes or until desired doneness, turning them over half way though.
When your onions are ready, pour in the beef broth and remaining tablespoon of Worcestershire sauce. Simmer for just a minute.
Serve the burgers on rolls with lettuce and shredded Swiss cheese. Top with the golden onions.