01 - Heat butter and olive oil in a large skillet over medium-low heat. Add sliced onions and salt. Cook, stirring occasionally, for 20–25 minutes until onions are golden and caramelized. Add sugar if desired to accelerate browning. Remove from heat and set aside.
02 - In another skillet, heat butter and olive oil over medium heat. Add mushrooms and cook for 5–7 minutes, stirring occasionally, until browned and tender. Add minced garlic and cook for 1 minute more. Season with salt and pepper. Remove from heat.
03 - In a bowl, gently combine ground beef with salt, pepper, and Worcestershire sauce. Divide into 4 equal portions and shape into patties slightly larger than your buns to account for shrinkage during cooking.
04 - Heat a grill pan or skillet over medium-high heat. Cook patties for 3–4 minutes per side for medium doneness. Place cheese slices on patties during the final minute of cooking to melt. Let patties rest for 1 minute before assembling.
05 - Lightly toast the buns, cut side down, in a dry pan or on the grill until golden and crisp.
06 - Layer lettuce on the bottom bun, add the beef patty, top with caramelized onions and sautéed mushrooms. Add tomato slices and condiments as desired. Complete with the top bun and serve immediately.