Prepare the Rice: Rinse the rice thoroughly under cold water until the water runs clear. Cook the rice according to your rice cooker's instructions or by using the stovetop absorption method. Once cooked, fluff with a fork and keep warm.
Make the Hamburger Patties: In a medium bowl, gently combine the ground beef with salt, pepper, garlic powder, and onion powder. Be careful not to overmix. Divide the mixture into four equal portions and shape them into patties, slightly larger than your rice bowls, about 1/2 inch thick. Create a slight indentation in the center of each patty to prevent them from puffing up too much during cooking.
Cook the Patties: Heat a large skillet (cast iron works best) over medium-high heat. Add the patties and sear for about 3-4 minutes per side, or until cooked to your desired doneness. Remove the patties from the skillet and set aside, leaving any drippings in the pan.
Prepare the Gravy: Reduce the heat to medium. Add the butter to the same skillet and let it melt. Whisk in the flour until smooth, cooking for about 1 minute to form a roux. Gradually whisk in the beef broth, ensuring no lumps form. Stir in the Worcestershire sauce, soy sauce, and black pepper. Bring the gravy to a simmer, stirring occasionally, until it thickens to your desired consistency, about 5-7 minutes. Taste and adjust seasoning with salt if needed.
Fry the Eggs: While the gravy is simmering, heat the vegetable oil or butter in a separate non-stick skillet over medium heat. Crack the eggs into the skillet and fry them sunny-side up, over-easy, or to your preference, until the whites are set and the yolks are still runny. Season lightly with salt and pepper.
Assemble the Loco Moco: Place a generous scoop of cooked rice into each serving bowl. Top each mound of rice with a hamburger patty. Spoon a generous amount of the hot gravy over the patty and rice. Finally, carefully place a fried egg on top of each Loco Moco.