In a large saucepan, combine chicken broth, water, and ginger slices. Cover and bring the broth to a gentle simmer, then turn off the heat. Cut the bok choy into small pieces and set aside.
Combine pork, scallions, ginger and garlic in a mixing bowl. Add soy sauce, vinegar, sesame oil, salt, pepper and cornstarch and mix well with a rubber spatula.
Remove wonton wrappers from package and cover them with damp paper towel to keep them from drying out. Assemble the wontons,(see below) place them on a large plate or baking sheet lined with waxed paper and cover them loosely with plastic wrap.
Bring chicken broth to boil. Use slotted spoon to add the wontons a few at a time, keeping the broth at a low boil. Cook wontons until they are no longer pink inside (remove one, cut open to check,) at least 7 minutes. Turn heat to high, add the bok choy, cover and cook for 3 minutes. Turn off heat and add pepper to taste.
Transfer 5 or 6 wontons to each soup bowl and ladle on the hot broth.
Wontons: Place a wrapper flour side up on your work surface. Using a spoon and a chopstick, drop a scant teaspoon of meat mixture onto wrapper. Moisten all edges of wrapper with a wet fingertip, then fold it over so edges meet (diagonally.) Pinch edges to seal them. Using your finger or a chopstick, make an indentation in the middlge of filled wonton. Dab drop of water on the corners and fold them in so they overlap above the indentation. Pinch them together to secure them in place.
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