Cook yucca in boiling salted water in a Dutch oven 30 minutes or until fork-tender. Dry thoroughly with paper towels, and spread on baking sheets to cool. Cut each into 1/4-inch-thick fries, and set aside.
Combine mayonnaise, next 4 ingredients, and, if desired, cayenne pepper in a small bowl.
Pour oil to depth of 3 inches into a Dutch oven, and heat to 350°. Fry yucca, in 3 or 4 batches, 6 minutes per batch. Drain on paper towels. Return oil to 350°, and fry yucca, in 3 or 4 batches, another 6 minutes or until crispy. Drain on paper towels, and season with additional salt, if desired. Serve with cilantro mayonnaise.