In a medium saucepan, combine the bananas with the vegetable stock, onion, water, pickled jalapeño, garlic and ginger and bring to a boil. (I misread the recipe so I included 1 cup ketchup, basil and pickling liquid in the boiling pot.) Simmer over moderate heat, stirring, until the bananas and onion are very tender, 15 minutes. Transfer to a blender and let cool slightly. Add an additional 1/2 cup of ketchup. Scrape the banana ketchup into a bowl and season with salt and pepper. Cover and refrigerate until chilled, about 30 minutes.

Step 2 Meanwhile, Make the Fries

Bring a large saucepan of salted water to a boil. Peel the yucca and cut into 3-inch lengths. Cut the lengths into 1/2-inch-thick wedges. Cook the yucca in the boiling water until tender, 10 to 15 minutes. Drain well and spread on a baking sheet to cool and dry; discard any stringy pieces of yucca.

Step 3 

In a large saucepan, heat 1 1/2 inches of oil to 360°. Set a rack over a baking sheet. Working in batches, fry the yucca, stirring gently to separate the wedges, until golden brown and crisp, 5 to 7 minutes. Using a slotted spoon, transfer the wedges to the rack and season generously with salt. Serve right away with the banana ketchup and lime wedges.

The banana ketchup can be refrigerated for up to 10 days.