Combine ground chicken, rice vinegar, soy sauce, sesame oil, grated garlic, ginger, brown sugar, and green onions in a mixing bowl. Mix until well combined.

Take a wonton wrapper and place about a teaspoon of the filling in the center. Moisten edges with water and fold to seal. Repeat until all wontons are assembled.

In a large pot, heat chicken broth with minced garlic, dark soy sauce, and sesame oil until boiling. Reduce heat and add green onions and bok choy, allowing to soften for a few minutes.

In another pot, boil water and gently add wontons. Cook until they float and then simmer for an additional 2 minutes.

Using a slotted spoon, transfer wontons to the simmering broth. Stir gently to combine and garnish with additional green onions before serving.