In a large mixing bowl, combine ground chicken, chopped raw shrimp, thinly sliced green onions (the green parts only!), chopped cilantro, cornstarch, ginger paste, grated garlic cloves, sesame oil, rice wine vinegar, and low-sodium soy sauce. Use chopsticks or a spoon to mix very well.
In a large soup pot or Dutch oven, heat neutral oil over medium-high heat. When hot, add the reserved thinly sliced white part of the scallions, ginger paste, and grated garlic cloves. Cook, stirring occasionally. Add low-sodium chicken broth, then bring the mixture to a simmer.
Drop small spoonfuls of the dumpling mixture into the broth. These should be about 2 teaspoons each. Repeat until all of the filling is used up, then allow to cook. The chicken is not fully cooked yet.
Add thinly sliced bok choy and quartered wonton wrappers, then cook until the dumplings are fully cooked. Chicken is safe to eat when it reaches an internal temperature of 165°F. Stir in remaining soy sauce. Taste and adjust seasoning.
Divide the soup between bowls, then garnish with a drizzle of chili oil and fresh cilantro. Enjoy!