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 golden and deeply caramelized. Optionally, add sugar halfway through to enhance sweetness. Keep warm.
02 - In a large bowl, gently combine ground beef, salt, black pepper, Worcestershire sauce, and Dijon mustard. Form mixture into four equal-sized patties, handling meat with care to maintain texture.
03 - Preheat grill or skillet to medium-high. Cook patties 3 to 4 minutes per side for medium doneness. If using cheese, add a slice to each patty during the last minute of cooking and cover to melt.
04 - Toast the split burger buns cut side down until golden brown.
05 - Place lettuce on bottom bun, add cooked beef patty, caramelized onions, tomato slices, pickles, and condiments as desired. Close with top bun and serve immediately.