Combine the stock, 3 scallions (each cut into thirds), ginger pieces, sesame oil, and soy sauce in a large pot over medium heat.
Simmer for 15 minutes.
Meanwhile, cook the noodles according to package directions. Set aside.
Use a slotted spoon to remove the ginger and scallion pieces and discard them.
Gently add the meatballs and bok choy to the soup and cook for 10 minutes, until meatballs are heated through and bok choy has softened.
Divide the drained noodles among individual soup bowls.
Ladle the soup, including meatballs and bok choy, around the noodles.
Top each bowl with sliced scallions and a pinch of red pepper flakes, if desired.
Serve at once, and enjoy!