To make the infused water, in a bowl, combine the ginger, scallions, and warm water, mix gently to release the flavor, then remove the solids and set the infused water aside.
To make the filling, in a bowl, add the chicken and sprinkle in the salt first, then mix until absorbed. Add the white pepper, soy sauce, oyster sauce, rice wine, and cornstarch, and mix well. Gradually add the infused water in two parts, mixing in one direction until fully absorbed, then stir in the scallions until combined.
To fill the pastry bag, transfer the filling into a pastry bag or zip-top bag and cut a small opening at the tip.
To wrap the wontons, place a wonton wrapper in your hand, pipe the filling into the center, brush the edges lightly with water, then pinch and seal. Repeat with the remaining wrappers.
To make the broth, in a pot over high heat, bring the chicken stock to a boil, then season with the salt, soy sauce, sesame oil, and white pepper.
To cook the bok choy, in a pot over high heat, bring water to a boil, blanch the bok choy for about 30 seconds, then remove and set aside.
To cook the wontons, in the same pot over medium heat, bring the water back to a gentle boil, add the wontons and stir gently, cook for 2 minutes, pour in 1 cup of cold water, then cook for another 2 minutes until the wrappers are translucent and the filling is fully cooked.
To serve, transfer the wontons to bowls, ladle in the hot broth, and top with the bok choy.