In a large bowl, combine the ground beef with Worcestershire sauce, garlic powder, onion powder, dried parsley, salt, pepper, and paprika. Mix gently until just combined; avoid overworking the meat to keep the patties tender. Form the mixture into four equal-sized patties.
Heat the vegetable or canola oil in a large skillet over medium-high heat. Once hot, add the beef patties and cook for about 4-5 minutes on each side until browned and cooked to desired doneness. Remove patties and set aside.
In the same skillet, reduce heat to medium and melt the unsalted butter. Add chopped mushrooms and onion (if using) and sauté until soft and golden, about 5 minutes. Stir in minced garlic and red pepper flakes, cooking for an additional minute until fragrant.
Sprinkle flour over mushroom mixture and stir to combine, cooking for 1-2 minutes. Gradually whisk in beef broth, ensuring no lumps. Add soy sauce, Worcestershire sauce, beef bouillon, Dijon mustard, dried parsley, thyme, and sesame oil. Bring gravy to simmer and cook until thickened, about 5-7 minutes. Season with salt and pepper to taste.
In a separate skillet, heat a drizzle of olive oil over medium heat. Crack eggs into the pan and cook until whites are set and yolks are runny, about 3-4 minutes.
To serve, place a generous scoop of cooked jasmine rice on a plate. Top with a beef patty, followed by a sunny-side-up egg. Generously ladle gravy over the top and garnish with sliced green onions.
