To prepare dumplings, cook cabbage in boiling water 1 minute or until tender. Drain and rinse with cold water; drain. Cool; chop.
Place mushrooms in a small bowl; cover with boiling water. Cover and let stand 30 minutes or until tender. Drain mushrooms; chop.
Combine cabbage, mushrooms, 1/4 cup green onions, 2 tablespoons cornstarch, and next 7 ingredients (through egg white) in a large bowl. Cover and refrigerate 4 hours.
Working with 1 gyoza skin at a time (cover remaining gyoza skins to prevent drying), spoon 2 teaspoons pork mixture into center of each skin. Moisten edges of gyoza skin with water. Fold in half, pinching edges together to seal. Place dumpling, seam side up, on a baking sheet sprinkled with remaining 1 teaspoon cornstarch (cover loosely with a towel to prevent drying). Repeat procedure with remaining gyoza skins and filling.
Heat 1 tablespoon canola oil in a large nonstick skillet over medium-high heat. Add 12 dumplings to pan; cook 3 minutes. Add 1/3 cup water. Reduce heat, and simmer 3 minutes or until water evaporates. Repeat procedure with remaining canola oil, dumplings, and water.
To prepare the sauce, combine 3 tablespoons chopped ginger and remaining ingredients in a small bowl. Serve sauce with dumplings.