Bring broth to a boil in a large pot.
Smash the sliced ginger with the side of a knife to bring out the flavor. Add it to the pot along with garlic. Cover and cook for 5 minutes.
Add the bok choy and partially cook for five minutes. Add the frozen wontons and mushrooms. Simmer for 2-3 minutes until wontons are heated through and bok choy is tender and wilted.
Stir in soy sauce and sesame oil.
Divide into 4 bowls and garnish with fresh onions.