Preheat an oven to (170°F/77°C) to keep the patties hot after you sear them and while you prepare the gravy.

In a large mixing bowl, combine the grated onion, crushed garlic, the beaten egg, soy sauce, salt, and black pepper. Whisk these together to create a loose paste.

Add the ground chuck and bread crumbs to the seasoning paste and mix with your hands just until combined.Portion the meat into 4 meatballs of equal size and place them on a sheet pan.

Flatten the balls into patties about ¾ to 1-inch thick and oval in shape.Cover and leave the patties at room temperature for at least 30 minutes to allow the seasoning to penetrate the meat. If you plan to marinate them longer, wrap the pan well and keep them in the fridge.

Begin steaming the white rice before you sear the burger patties.

Preheat a 12 to 14-inch cast iron skillet over medium heat. Press the patties into the skillet once it feels hot when you hold your hand over it.

Sear the meat for 3-4 minutes on the first side without moving it, so it develops a nice, brown crust. A spatula should meet little resistance when you slide it under the patty.Let the meat sear a minute or two longer if the spatula cannot get under the meat easily.

Flip the patties and sear for 3-4 minutes on the other side. Transfer the meat from the pan and set it on a clean sheet pan. Put the sheet pan in the warm oven while you prepare the brown gravy.

Strain the fat from the frying pan into a heat-safe separate bowl. Return the rendered fat to the pan and heat it over medium heat.

Sprinkle all-purpose flour over the fat and whisk them together to create a tan-colored paste. Cook this roux for 2-3 minutes on low heat, constantly whisking, until it begins bubbling and becomes the color of peanut butter.

Gradually pour the beef stock into the roux, constantly whisking to avoid creating lumps in the gravy. Heat the gravy for 4 to 5 minutes, frequently whisking, until it thickens. Season the gravy with soy sauce, salt, and black pepper to taste. Keep the gravy warm while you assemble the rest of the dish.

Add a small amount of oil large skillet and heat it over medium-high heat. Add the eggs to the oil in the pan and fry them until the edges are crispy and browned and the egg white is opaque- about 3 minutes.

Spoon a cup of steamed rice onto each plate.Nestle the beef patties on the rice and pour a generous amount of the warm gravy over each one.Top the patties with the fried eggs and garnish with thinly sliced green onions.