In a medium pot or Dutch oven, heat the vegetable oil over medium heat. Add the garlic, ginger and white parts of the scallions and cook, stirring frequently, until fragrant, 1 to 2 minutes. Add the shiitakes and cook until they begin to soften, another minute.
Add the bone broth and bring to a boil. Add the bok choy and simmer, stirring occasionally, until the bok choy is tender, 4 to 5 minutes. Add the soy sauce and stir. Add the wontons and cook until they are cooked through, 2 to 3 minutes. Taste and season if necessary.
Ladle into bowls, then top with the scallion greens. Serve immediately.
Wonton soup is a staple in Chinese cuisine. Here, I'm keeping all the traditional flavors, but store-bought broth and wontons make it an easy and delicious weeknight meal.