Make the wonton filling. In a large mixing bowl, combine 1 lb ground chicken, 1 lb chopped raw shrimp, thinly sliced green onions (the green parts only!), chopped cilantro, 1 Tbsp cornstarch, 2 tsp ginger paste, 2 grated garlic cloves, 2 tsp sesame oil, 2 tsp rice wine vinegar, and 2 tsp low-sodium soy sauce. Use chopsticks or a spoon to mix very well. Allow this to come to room temperature while you make the broth.
Make the broth. In a large soup pot or Dutch oven, heat 2 tsp neutral oil over medium-high heat. When hot, add the reserved thinly sliced white part of the scallions, 2 tsp ginger paste, and 2 grated garlic cloves. Cook, stirring occasionally, for 1-2 minutes. Add 4 cups (32oz) of low-sodium chicken broth, then bring the mixture to a simmer.
Add the dumpling mixture. Once simmering, reduce the heat to medium. 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 for 5 minutes. The chicken is not fully cooked yet.
Stir in veggies. Add thinly sliced bok choy and quartered wonton wrappers, then cook for an additional 7-10 minutes more, or until the dumplings are fully cooked. Chicken is safe to eat when it reaches an internal temperature of 165°F. Stir in remaining 2 tsp soy sauce. Taste and adjust seasoning, adding a splash of soy sauce or vinegar as needed.
To serve: Divide the soup between bowls, then garnish with a drizzle of chili oil and fresh cilantro. Enjoy!