To prepare the soup:
In a large saucepan heat the oil on medium until hot. Add the garlic and ginger and cook for about 2 minutes (until it smells awesome). Add the chicken broth and scallions. Reduce to medium low and allow to simmer for about a half hour while you prepare the wontons
Traditionally speaking, wonton soup is made with chicken bouillon as well as chicken broth. Sometimes a little soy sauce too. This can be a little salty, but its good if you feel your broth needs a little more flavor
To prepare the wontons:
Combine the chicken, scallions, ginger, soy sauce, cornstarch, sesame oil, salt and pepper in a bowl and set aside.
Arrange 8 wonton wrappers on a work surface. Place 1 tsp of the chicken mixture in the center of each wrapper. About a grape sized amount. Moisten the edges of each wonton wrapper and pull one off the of the top corners diagonally over the fillin to make a triangle. Press the edges firmly to seal. Overlap the tips of these corners, moisen with water, and press together. You should have a little wonton "package" with a pointy tip.
Place completed wontons on a baking sheet lightly covered with cornstarch and cover with a damp paper towl. Repeat with the remaining filling and wrappers making 16 wontons.
Add the mushrooms to the broth about 2-3 minutes before the wonton.
Add the wonton and bok choy to the soup and cook for about 10 minutes until the wontons are cooked through and the bok choy is tender.
1 cup of broth with 4 wontons makes a great starter soup.
*Note: If you have dried shiitake mushrooms you can add these to the broth when you add the scallions and they give the broth a really nice authentic flavor.