In a food processor, combine the shrimp, cabbage, carrots, green onions, garlic, ginger, soy sauce, sesame oil, and cornstarch. Pulse until the mixture is well combined but still slightly chunky.

Place a dumpling wrapper on a clean surface. Spoon about 1 tablespoon of the shrimp mixture into the center of the wrapper. Moisten the edges with water, fold the wrapper in half, and pinch to seal. Repeat with remaining wrappers and filling.

In a large skillet, heat 2 tablespoons of cooking oil over medium heat. Arrange the dumplings in a single layer in the skillet and cook for 2-3 minutes or until the bottoms are golden brown.

Carefully add 1/4 cup of water to the skillet and cover immediately. Steam the dumplings for about 5-7 minutes or until the shrimp is cooked through and the wrappers are tender.

Remove the lid and let the dumplings cook for another minute to crisp up the bottoms. Serve hot with soy sauce or your favorite dipping sauce.