Cook the rice: Combine the rinsed rice, water, and 1/2 teaspoon salt in a medium saucepan. Bring to a boil over medium-high heat. Stir once, cover tightly, reduce the heat to low, and cook for about 15 to 18 minutes, until the water is absorbed.

Rest the rice: Remove the saucepan from the heat without lifting the lid. Let the rice rest, covered, for 10 minutes. Fluff gently with a fork before serving.

Season the beef: While the rice cooks, place the ground beef in a large bowl. Add the Worcestershire sauce, soy sauce, garlic powder, onion powder, black pepper, and salt. Mix gently just until the seasonings are distributed.

Shape the patties: Divide the beef mixture into 4 equal portions. Shape each portion into a patty about 4 inches (10 cm) wide and 1/2 inch (1.25 cm) thick. Press a shallow indentation into the center of each patty to reduce doming during cooking.

Heat the skillet: Place a 12-inch skillet over medium-high heat. If the beef is very lean or the skillet is not well seasoned, add the neutral oil.

Cook the first side: Add the patties in a single layer. Cook without moving them for 3 to 4 minutes, until the undersides are deeply browned and release easily from the skillet.

Finish the patties: Turn the patties and cook for another 3 to 5 minutes, until browned and the centers reach 160°F (71°C). Transfer the patties to a clean plate and cover loosely to keep warm.

Cook the onions: Reduce the skillet heat to medium. Pour off excess grease, leaving about 1 tablespoon in the pan. Add the butter and sliced onion. Cook for 5 to 7 minutes, stirring occasionally, until the onion is soft and golden.

Make the roux: Sprinkle the flour over the onions and stir continuously for 1 minute. The onions should look lightly coated, with no dry flour remaining.

Add the broth: Gradually whisk in about 1/2 cup (120 ml) of the beef broth until smooth, scraping up the browned bits from the bottom of the skillet. Slowly whisk in the remaining broth.

Season and thicken the gravy: Add the Worcestershire sauce, soy sauce, black pepper, and salt. Bring to a gentle simmer and cook for 4 to 6 minutes, stirring frequently, until the gravy thickens enough to coat the back of a spoon.

Return the patties to the gravy: Place the cooked beef patties back into the skillet and spoon some gravy over them. Keep warm over low heat for 2 to 3 minutes while cooking the eggs.

Fry the eggs: Melt the butter in a clean skillet over medium-low heat. Crack in the eggs and cook until the whites are fully set and the yolks reach the desired doneness. For fully cooked eggs, continue until the yolks reach 160°F (71°C). For soft yolks, use pasteurized eggs.

Assemble the loco moco: Divide the warm rice among four plates or shallow bowls. Place one beef patty over each portion of rice.

Add the gravy and eggs: Spoon the hot onion gravy generously over each beef patty and some of the rice. Top each serving with one fried egg.

Garnish and serve: Sprinkle with sliced green onions and parsley, if using. Serve immediately while the gravy and rice are hot.