To make the filling: In a large mixing bowl, combine the ground pork, oyster sauce, dark soy sauce, sesame oil, egg, and cornstarch until well mixed. Add the carrots, cabbage, and scallions, then continue mixing until the filling becomes slightly sticky.
To assemble the blanket dumplings: With the heat off, add the cooking oil to a large nonstick pan. Scoop 9 portions of the filling into the pan, leaving a little space between each one. Lay a wonton or dumpling wrapper over each mound like a little blanket, gently pressing it so it hugs the filling.
To pan-fry the dumplings: Place the pan over medium heat and cook for about 1 minute, until the pork filling begins to set.
To steam the dumplings: Carefully pour the water into the pan. While you add the water, partially cover the pan to help contain the hot oil splatter. Once all the water has been added, cover the pan completely and steam for about 5 minutes, or until the pork reaches an internal temperature of 160°F (71°C).
To crisp the dumplings: Remove the lid and continue cooking for about 2 minutes, until the water has evaporated and the bottoms are golden and crispy.
To finish and serve: Turn off the heat and sprinkle the scallions over the dumplings. Drizzle the soy sauce and chili oil directly into the pan, or serve them on the side as a dipping sauce. Serve immediately.