In a mixing bowl, combine ground meat, beaten egg, breadcrumbs, salt, and pepper. Mix well until combined.

Shape the mixture into small patties and refrigerate until ready to cook.

Heat salad oil in a frying pan over medium heat. Cook the patties on both sides until browned and cooked through.

In the same pan, add ketchup, Worcestershire sauce, mirin, soy sauce, water, and butter. Stir well to create the sauce.

Add the bean sprouts to the pan and cook briefly until slightly softened.