1.Heat butter in a large frying pan over medium heat. Add onions, cook, stirring, until golden and caramelised (about 15 minutes). Cool.
2.Meanwhile, pulse the beef in a food processor, in two batches, until coarsely minced (or the coarse plate of a mincer, if you have one).
3.Combine the beef, onions, egg, breadcrumbs and Worcestershire sauce in a large bowl. Season with salt and freshly ground black pepper; mix well. Form mixture into four patties.
4.Heat oil in a large frying pan over medium-high heat; cook patties, turning once, until just cooked through. Top patties with cheese during the last minute of cooking and allow the cheese to melt.
5.Toast the cut sides of the buns. Divide lettuce, patties, relish, pickles and tomato among bun bases; sandwich with bun tops.
Uncooked beef patties suitable to freeze. Not suitable to microwave.Note