1. Heat 2 tablespoons of oil in a large frying pan over medium heat. Add sliced onions and season with salt. Sauté for 5 to 7 minutes until lightly browned, then reduce heat to low and cook, stirring occasionally, for 20 to 25 minutes until onions are deeply caramelized. Set aside.
2. Form the ground beef into four equal-sized patties (about 4 ounces or 113 grams each). Season both sides with salt and pepper, and optionally mix in some Worcestershire sauce and steak seasoning.
3. Heat the remaining 2 tablespoons of oil in a separate large skillet, griddle, or cast iron pan over medium heat (or preheat a grill to medium-high, 350-400°F). Cook patties for 5 to 7 minutes per side for medium doneness, avoiding pressing down on the patties to retain juices. Add Swiss cheese slices during the last 2 to 3 minutes of cooking until melted. Remove patties and let rest 3 to 5 minutes.
4. In the skillet with rendered beef fat, add sliced mushrooms and a pinch of salt; sauté on high heat for 5 to 7 minutes until browned. Add garlic and Worcestershire sauce (about 1 tablespoon if using), stirring until fragrant. Pour in beef stock and simmer until reduced by half and slightly thickened (approximately 8 to 10 minutes). Season with salt, pepper, and add optional butter and fresh parsley.
5. Toast buns separately, either on grill or in oven, brushing with oil if desired to prevent sogginess.
6. Assemble each burger by placing the rested beef patty on the bottom bun, topping with caramelized onions and mushroom sauce, then finishing with the top bun.