01 - Heat butter and olive oil in a large skillet over medium-low heat. Add sliced onions and salt. Cook slowly, stirring frequently, for 25 to 30 minutes until deeply golden and caramelized. Add sugar halfway through, if desired, to enhance sweetness. Keep warm when done.
02 - In a large mixing bowl, gently combine ground beef, salt, black pepper, Worcestershire sauce, and Dijon mustard. Form into 4 equal patties, handling the meat minimally to maintain tenderness.
03 - Preheat grill or skillet to medium-high heat. Cook patties for 3 to 4 minutes per side for medium doneness. If using cheese, place slice atop each patty in the final minute of cooking and cover to melt.
04 - Place burger buns cut side down on the grill or skillet and toast until golden brown.
05 - On the bottom bun, arrange lettuce, followed by a beef patty, caramelized onions, tomato slices, pickles, and chosen condiments. Top with the bun and serve promptly.