To blanch the Napa cabbage: Bring a large pot of water to a boil. Add the green leafy portions of the Napa cabbage leaves and blanch for about 30 seconds, until softened. Remove, drain well, and set aside.
To make the filling: In a large mixing bowl, combine the ground chicken, oyster sauce, dark soy sauce, sesame oil, egg, and cornstarch. Mix until well combined. Add the scallions and mix again until evenly distributed.
To assemble the blanket dumplings: With the pan off the heat, add the cooking oil. Divide the chicken filling into 9 portions directly in the pan, leaving a little space between each one. Place a blanched Napa cabbage leaf over each portion like a blanket, then gently shape the Napa cabbage around the top and sides. There is no need to fold or seal it; the bottom of the chicken remains directly against the pan.
To pan-fry the blanket dumplings: Place the pan over medium heat and cook for about 1 minute, until the bottoms of the chicken begin to set.
To steam the blanket dumplings: Carefully pour the water into the pan. Cover and cook for about 6 minutes, or until the chicken is completely cooked through and reaches an internal temperature of at least 165°F (74°C).
To crisp the bottoms: Remove the lid and continue cooking for about 1 minute, until the excess water has evaporated and the bottoms are golden.
To serve: Finish with the sliced scallion, soy sauce, and chili oil. Serve immediately.