Prep the Cabbage: Bring a large pot of water to a boil. Blanch the napa cabbage leaves for 30 seconds until just softened. Remove and pat dry with paper towels. Trim the thick stems for easier folding if needed.
Make the Filling: In a large bowl, combine the ground pork, green onions, garlic, carrots, shiitake mushrooms, vegetarian oyster sauce, cornstarch, soy sauce, and sesame oil. Mix until well combined.
Assemble the Dumplings: Lay a cabbage leaf flat. Spoon 1–2 tablespoons of filling into the center. Fold the sides over the filling, then roll from the bottom to form a tight bundle. Repeat with remaining leaves.
Cook the Dumplings: Pan-fry Method: In a large non-stick pan, add a bit of oil and place dumplings seam-side down. Add ¼ cup of water, cover with a lid, and cook over medium heat until the water evaporates and the bottoms are golden and crispy (about 8–10 minutes).
Steam Method: Steam the dumplings in a lined steamer basket for 10 minutes, or until the it is fully cooked through.
Serve: Enjoy warm with the dipping sauce