01 - Heat butter and olive oil in a large skillet over medium heat. Add sliced onions, salt, and sugar. Cook, stirring occasionally, until onions are deeply golden and caramelized, about 15-18 minutes. Stir in balsamic vinegar if using, cook 1 minute more, then set aside.
02 - While onions cook, gently mix ground beef with Worcestershire sauce, salt, and pepper. Form into 4 equal patties, about 3/4 inch thick. Press a slight indentation in the center of each patty.
03 - Preheat grill or skillet over medium-high heat. Cook patties for 3-4 minutes per side for medium doneness. Top each with a slice of Swiss cheese during the last minute of cooking; cover to melt.
04 - Toast buns cut side down until golden.
05 - Spread mayonnaise on bottom buns (if using). Add lettuce, tomato, a beef patty with melted Swiss, caramelized onions, and pickles. Top with upper buns and serve immediately.