In a large bowl, combine shredded cabbage, grated carrot, chopped mushrooms, chopped green onions, minced garlic, grated ginger, soy sauce, toasted sesame oil, and ground black pepper. Mix well until all ingredients are evenly incorporated.
Place one dumpling wrapper on a clean surface. Spoon about 1 tablespoon of the vegetable filling into the center of the wrapper.
Moisten the edges of the wrapper with a little water using your fingertip.
Fold the wrapper in half over the filling to create a half-moon shape. Press the edges firmly to seal, making small pleats along the edge if desired to secure the dumpling.
Repeat the filling and folding process with the remaining wrappers and filling.
Preheat the air fryer to 375°F (190°C) for 3 minutes.
Lightly brush each dumpling with vegetable oil on both sides to help achieve a crispy texture.
Place dumplings in a single layer in the air fryer basket, making sure they do not touch. You may need to cook in batches depending on the size of your air fryer.
Air fry the dumplings at 375°F (190°C) for 10 to 12 minutes, flipping them halfway through cooking, until they are golden brown and crispy.
Remove the dumplings from the air fryer and let them cool slightly before serving.
Serve the air fryer vegetable dumplings warm with soy sauce or your favorite dipping sauce.