01 - Heat butter and olive oil in a large skillet over medium heat. Add sliced onions and salt. Cook, stirring occasionally, for 20–25 minutes until deep golden brown. Add sugar after 10 minutes if using. Reduce heat if onions brown too quickly. Set aside.
02 - In a large bowl, gently mix ground beef with Worcestershire sauce, garlic powder, salt, and pepper. Form into 4 equal patties, slightly larger than the buns; make a shallow dimple in the center of each patty.
03 - Preheat a grill or skillet over medium-high heat. Cook patties 3–4 minutes per side for medium, or to desired doneness. Add cheese slices during the last minute of cooking, cover to melt.
04 - Lightly toast buns cut side down on grill or in a dry skillet until golden.
05 - Place lettuce on the bottom bun, add burger patty, top with caramelized onions, tomato, pickles, and desired condiments. Cap with the top bun and serve immediately.