Rinse the rice under cool water until the water runs clear. Combine rice with 2 cups of water in a rice cooker and cook on the regular setting. Let it sit for 5 minutes to fluff up before serving.

In a medium saucepan over medium heat, whisk together beef stock, cornstarch, onion powder, shoyu, and beef bouillon paste. Stir continuously until thickened, about 5-7 minutes. Remove from heat and stir in heavy cream.

In a bowl, mix ground beef, egg, panko, ketchup, mayonnaise, and a pinch of salt and pepper. Form into 4 patties. Heat a skillet over medium-high heat, add oil, and cook the patties for about 5 minutes on each side until cooked through.

In a separate non-stick pan, heat cooking oil over medium heat. Crack eggs into the pan and season lightly. Cook until whites are set and edges are crispy, about 2-3 minutes. For over-easy eggs, flip and cook for an additional 30 seconds.

To plate, scoop a portion of rice onto a dish, place a burger patty on top, drizzle with gravy, and crown with an over-easy egg.