Peel the yucca, cut it into 3- to 4-inch sections and quarter it lengthwise. Lay the quarters with a cut side down and slice off the core; discard. Cut cored quarters into 1-inch pieces. Put the yucca in a medium saucepan with cold water to cover over medium-high heat, cover and bring to a boil. Cook until the yucca is soft, about 30 minutes. Strain through a colander and let sit until cool enough to handle, about 5 minutes. Return the yucca to the saucepan and mash with a potato masher until uniform in texture; do not worry if some of the pieces are a bit lumpy. Season with 1 1/2 teaspoons salt.
Roll rounded tablespoon-sized scoops of yucca into balls and place on a sheet pan. Make an indention in each ball with your thumb, stuff the hole with a large pinch of cheese, then pinch each ball closed and roll to smooth the edges.
Fill a large pot or Dutch oven with 3 inches of vegetable oil and heat over medium-high heat until it reaches 360 degrees F.
Crack the egg into a small bowl and whisk in 1 tablespoon water to make an egg wash. Put the breadcrumbs in a second small bowl. Roll each ball until coated in the beaten egg and then in the breadcrumbs. Drop 5 or 6 yucca balls into the oil and cook until golden brown, 3 to 4 minutes. Drain on paper towels and sprinkle with salt. Repeat with the remaining balls. Serve the fritters hot with lime wedges or fresh mojo sauce.
Frying on the stovetop is as much an art as a science. Keep in mind that when adding a large quantity of items into oil for frying, the temperature will drop (since the items range from cold to room temperature, say 40 to 80 degrees F). In this recipe we start at a slightly higher temperature (360) than we intend to fry at (350). By the time you have added enough yucca balls to the oil, the temperature will be just right.
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