Whisk together first 7 ingredients in a small bowl. Place fish in a plastic zip-top bag; add 1/4 cup soy mixture, and seal bag. Marinate at room temperature 20 minutes, turning bag occasionally. Toss carrot and green onions with 2 tablespoons soy mixture; set remaining mixture aside.
Rinse cabbage under cold water. Place wet leaves in a medium microwavable bowl; cover and vent. Microwave at HIGH 1 to 2 minutes or until leaves are pliable. Drain leaves, and cool slightly.
Place 4 cabbage leaves on work surface. Spoon 2 tablespoons carrot mixture into center of each leaf. Remove fish from bag, discarding liquid. Place a fillet over carrot mixture; top each fillet with 2 more tablespoons carrot mixture. Top with remaining 4 cabbage leaves, and wrap tightly into bundles. Tie with string.
Fill a Dutch oven with water to the depth of 1 inch. Add ginger and mint to water; place steamer basket over water. Bring water to a simmer. Place bundles in steamer basket; cover and steam 10 to 12 minutes.
Remove bundles, and let stand 1 minute; transfer to serving plates, and remove string. Spoon remaining soy mixture evenly over bundles.