Mix the ground pork, egg, cornstarch, 2 teaspoons of sesame oil, ginger, monosodium glutamate, salt, and half of the chopped green onions together in a bowl. Use your hands to mix until the ingredients are evenly distributed. Set aside.
Heat the vegetable oil in a wok or large skillet over high heat. When the oil is hot, fry the napa cabbage, stirring constantly, until cabbage begins to wilt, 2 to 3 minutes. Pour in the chicken broth, water, and soy sauce. Bring to a boil, then lower the heat to medium.
Use a spoon to form the meat mixture into 1 inch balls. Drop them into the boiling soup. When the last ball has been added, cover with a lid and simmer for 10 minutes. Taste, and adjust salt before serving. Garnish with remaining green onions and a drizzle of sesame oil.