Prepare the Beef Mixture

In a mixing bowl, combine the ground beef with the finely chopped onion, grated garlic, 1½ teaspoons Worcestershire sauce, kosher salt, and black pepper. Mix gently with your hands or a wooden spoon, taking care not to overwork the mixture. Shape the mixture into four patties, each about ½-inch thick. Place the patties on a plate, cover with plastic wrap, and refrigerate for 20 minutes.

Caramelize the Onions

Heat 1 tablespoon of oil in a large skillet over medium heat. Once the oil shimmers, add the sliced onion. Sauté for 5-7 minutes, stirring occasionally, until the onion softens and begins to turn translucent. Lower the heat and continue cooking for about 10 minutes, stirring frequently, until the onions are fully caramelized. Transfer to a bowl and set aside.

Cook the Patties

Add another tablespoon of oil to the skillet and heat over medium. Place the chilled patties in the skillet, ensuring even spacing. Sear for about 4 minutes per side until nicely browned. Remove the patties from the pan and allow them to rest on a clean plate.

Sauté the Mushrooms (Optional)

Heat the remaining ½ tablespoon of oil in the skillet over medium heat. Add the mushrooms, seasoning them with salt and pepper. Sauté for approximately 10 minutes until tender, then set aside.

Make the Gravy

Return the caramelized onions to the skillet, followed by the beef broth, soy sauce, and the remaining 1½ teaspoons Worcestershire sauce. Stir and bring the mixture to a gentle simmer. In a small bowl, whisk together the cornstarch with 2 tablespoons of the simmering broth until smooth. Gradually stir this slurry into the skillet, allowing the sauce to thicken over 5-7 minutes.

Assemble the Dish

Divide the steamed white rice among four plates. Top each portion with a cooked beef patty, ladle the gravy generously over the top, and crown with a fried egg. Garnish with chopped scallions before serving.