In a metal or bamboo steamer basket, steam monkfish for 2 minutes. Remove from steamer and halve. Place cabbage leaves in steamer basket and cook for 5 minutes or until tender.
Lay cabbage leaves on a flat surface. Place 3/4 teaspoon ginger, 1 tablespoon carrots, and 1/2 teaspoon chives on each cabbage leaf, followed by 1/2 fillet of monkfish. Season with a pinch of salt and pepper. Roll, folding in sides to enclose monkfish. Steam for 4 to 5 more minutes or until fish is cooked through.
Combine all ingredients for ponzu sauce in a blender container and puree. Strain, if desired. Serve 2 tablespoons ponzu sauce with 2 monkfish wraps.