Combine 1/3 cup water, chopped onion, and chopped garlic in a custard cup; set aside to soften for about 10 minutes.

Cut the ends off the green bananas and make cuts down the seams.

Place the bananas in a bowl of hot water; set aside for 10 minutes for easier peeling.

Peel the bananas and cut them into 1/4-inch thick slices (about 3 cups); place in a medium bowl.

Add 1 teaspoon of salt and enough water to cover the banana slices; set aside for 10 to 15 minutes.

In a large saucepan, heat vegetable oil until warm.

Add the onion mixture and cook until crisp-tender, about 3 to 4 minutes.

Add the minced tomatoes, 2 tablespoons of parsley flakes, bay leaf, red pepper, and remaining 3 teaspoons of salt; cook, stirring frequently, until the tomatoes are softened, about 4 minutes.

Add 6 cups of water; heat the stew until it is just below boiling.

In a small bowl, combine tapioca and 1/2 cup of water until smooth.

Add the tapioca mixture and bread crumbs to the stew, stirring constantly.

Add the white potatoes, sweet potatoes, shredded green cabbage, and the liquid-removed bananas; simmer, uncovered, until the vegetables are almost tender, about 35 minutes.

Add the tilefish chunks; cook until the fish is firm, about 5 minutes.

Remove the bay leaf; sprinkle with the remaining 1 teaspoon of parsley flakes before serving.