In a bowl, combine the chopped shrimp, ground chicken, 1/2 tablespoon soy sauce, sesame oil, cornstarch, grated garlic, grated ginger, half of the chopped green onion, sugar, and black pepper. Mix well until the ingredients form a uniform paste.
Place about 1 teaspoon of the filling onto the center of each wonton wrapper. Moisten the edges with water using your finger, then fold the wrapper to form a dumpling. Press firmly to seal and set aside on a lightly floured surface.
In a large pot, bring the chicken stock, ginger slices, smashed garlic, and dried shiitake mushrooms to a simmer over medium heat. Stir in the remaining 1/2 tablespoon soy sauce and the fish sauce. Let simmer for about 5 minutes to infuse the flavors. Adjust the flavor, adding more soy sauce if needed.
Gently add the prepared wontons into the simmering broth. Allow them to cook for 5-6 minutes until they float, indicating they are cooked through.
In a separate pot, blanch the egg noodles in boiling water for about 1 minute. In the last 2-3 minutes, add the bok choy to the pot. Drain and divide the noodles and bok choy among serving bowls.
Place 4-5 wontons on top of the noodles and vegetables. Carefully ladle the hot broth over the bowls, and garnish with the remaining chopped green onion.