Cook yucca in boiling salted water in a large pot for 30 minutes or until fork-tender. Dry thoroughly with paper towels, and spread on baking sheets to cool. Cut each into ¼-inch-thick fries, and set aside.
In a small bowl, combine the mayonnaise, cilantro, lime juice, garlic, salt and pepper. Cover and refrigerate until ready to use.
First Frying: Pour oil to depth of 3-inches in a large pot, and heat to 350°F. Fry the yucca, in 4 or 5 batches, 6 minutes per batch. Drain on paper towels.
Second Frying: Return the oil to 350°F. and fry the yucca, in 4 or 5 batches, another 6 minutes or until crispy. Drain on paper towels, and season with additional salt, if desired.