Rinse the white medium grain rice under cold water until it runs clear. Transfer to a rice cooker, add water, and cook until fluffy, about 20 minutes. Fluff with a fork once done and set aside.

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

In a mixing bowl, combine ground beef, egg, panko, ketchup, mayonnaise, salt, and pepper. Form evenly sized patties, about ½ inch thick. Cook in a skillet over medium heat for about 4-5 minutes on each side until fully cooked.

In another skillet, heat a small amount of cooking oil over medium heat. Crack the eggs and cook until the whites are set, about 3-4 minutes. For over-easy eggs, gently flip and cook for an additional 1-2 minutes.

To assemble, layer the fluffy rice on a plate, place a burger patty on top, ladle gravy over the patty, and top it with an over-easy egg. Serve immediately.