4Hamburger buns (if making doubles; 8 buns if making singles)
2tablespoons vegetable oil
1tablespoon sweet pickle relish
1/2teaspoon white vinegar
1cup shredded iceburg lettuce
8slices American cheese
Heat oil in pan and add onions. Cover onions and cook over medium heat for 30 minutes or until onions begin to turn golden brown and caramelize. Watch them so they don’t burn. Remove lid and cook for 5 more minutes; add 1/2 cup water. Allow water to cook out. Set onions aside; they can be made several days ahead of time and refrigerated.
Mix together mayo, ketchup, relish and vinegar in a bowl and set aside.
Heat griddle and lightly brush with vegetable oil. Toast buns on griddle, split side down. After buns are toasted golden brown spread each bottom bun with 1 tablespoon of mayo mixture. Top with tomato and lettuce.
Form meat into 8 patties about 4 inches wide and 1/2 inch thick. Season both sides of hamburger patties with salt and pepper and cook on griddle for 3-5 minutes. Spread 1 1/2 teaspoons of mustard on the top, uncooked side of each patty and flip. Top patty with cheese and allow to cook until desired doneness.
Add hamburger to bun and top with caramelized onion.