Bring chicken broth to a boil in a large pot.
Smash the sliced ginger with the side of a knife to bring out the flavor and add to the pot with the garlic, cover and cook 5 minutes.
Add the bok choy and partially cook 5 minutes, then add the frozen wontons and mushroom, simmer for 2 to 3 minutes, until the wontons are heated through and bok choy is tender and wilted.
Stir in soy sauce and sesame oil.
Divide soup in four bowls. Garnish with fresh scallions.