Mix together the shrimp, ground beef or pork, green onion, soy sauce, sesame oil, salt, and a pinch of pepper.
Place half a tablespoon of filling in the center of a wonton wrapper. Fold the wrapper in half and seal with a bit of water. Bring the corners together and seal again with a bit of water.
Repeat until you have used all the filling (and freeze some of the wontons at this point, if desired).
Bring the chicken broth to a boil, adding the green onions, garlic cloves, and ginger. Once boiling, let it continue to boil for another 3 minutes to fully infuse the ginger and garlic.
Remove the ginger and garlic from the broth using a small strainer or spoon.
Next, add the bok choy and cook for another minute.
Add the wontons and cook for five minutes.
Serve hot.