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.