Cook the yuca in a large pot with salted water over medium heat for about 15 minutes or until fork tender.
Drain the yuca and remove any fibers from the center. Transfer to a large bowl and mash.
Place the eggs in a bowl. Place the breadcrumbs in another bowl.
Form 12 balls with the mash. Flatten them with your hands and place 1 piece of cheese in the center and form the ball again to cover the cheese.
Dip the balls into the beaten egg covering all sides, and then cover them with breadcrumbs.
Fill a large skillet with oil and heat over medium-high heat to 350F. Place the balls into heated oil and fry for 4 minutes or until brown on all sides, turning over once about halfway through. Remove from the oil and place on a plate lined with paper towels.