"Zen" refers to a style of Buddhism (most Buddhists are vegetarian, but not all), however this vegan dish is what Zen Buddhist monk might eat at temples throughout Japan. You can have them as an appetizer or a main course with a side of vegetables or tofu. You can keep make the dumplings up to a month in advance: Place uncooked dumplings on a baking sheet and freeze; store in zip-top freezer bags. To serve, steam the frozen dumplings for about 10 minutes or until the wonton wrappers are translucent.
To prepare dumplings, drop ginger and garlic through food chute with food processor on; process until minced. Add the asparagus, 1/4 cup green onion pieces, and water chestnuts; pulse 4 times or until chopped. Add mushrooms, 2 teaspoons sesame oil, 1 1/2 teaspoons soy sauce, and 1/4 teaspoon salt; pulse 4 times or until mixture is finely chopped.
Working with 1 wonton wrapper at a time (cover remaining wrappers with a damp towel to keep from drying), spoon about 2 teaspoons mushroom mixture in the center of wrapper. Moisten edges of wrapper with water. Bring 2 opposite corners together. Press edges together with fingertips to seal, forming a triangle. Place on a baking sheet coated with cooking spray while assembling; lightly cover with a towel or plastic wrap. Repeat procedure with remaining wonton wrappers and mushroom mixture.
Add water to a Dutch oven to a depth of 1 inch; bring to a boil. Coat a metal vegetable steamer with cooking spray. Arrange 9 dumplings in steamer, slightly overlapping. Steam dumplings, covered, 8 minutes or until tender. Remove dumplings from steamer; cover and keep warm. Repeat procedure with remaining dumplings.
To prepare sauce, combine 1/3 cup soy sauce and remaining ingredients. Drizzle over dumplings.