in a bowl combine the ground beef 1 teaspoon kosher salt, 1/2 teaspoon pepper, 1½ teaspoons of the Worcestershire sauce, onion and garlic. Gently mix with your hands or a wooden spoon just till combined, do not over mix it. Form into four equal-sized patties about 1/2 inch thick; ours were more like an inch. Set aside on a plate, wrap in plastic and place in the fridge for 20 minutes to rest.
In a large skillet add 1 tablespoon of oil and set over medium heat. When the oil is hot (shiny and shimmering), add the onion wedges and saute until translucent, 5-7 minutes. Turn the heat to low and continue cooking for 10 more minutes, stirring often. Cook until they are soft and caramelized. Transfer to a bowl and set aside.
In the same pan add 1 tablespoon of oil and set it over medium heat. When the oil is hot, swirl the oil around the pan to make sure the surface is covered. Gently place place the patties in the pan, leaving room around each one. Cook until browned, around 4 minutes each side. Using a spatula place the patties on a plate and set aside to rest.
add the remaining ½ tablespoon oil to the pan over medium heat until hot. Add the mushrooms and saute until tender, about 10 minutes. Season the mushrooms with salt and pepper, then add the reserved caramelized onions. Add the beef broth, soy sauce and the remaining Worcestershire sauce and bring it to a simmer. Turn the heat to medium-low, scoop out a tablespoon of the broth from the skillet, and whisk it with the cornstarch in a small bowl until smooth. Whisk the cornstarch slurry into the skillet and simmer until the sauce has thickened, 5-7 minutes.
place 1 cup of steamed rice on each plate and top, in order. 1 beef patty, some gravy, 1 fried egg, and chopped green onions before serving.