Bring a large pot of water to boil. Salt the water (about a tablespoon) and add the yuca. Cook according to the package instructions, or until fork tender (about 15-25 minutes).
Drain the yuca and remove the woody stems from the core. Season with salt and pepper and mash until smooth.
Take a heaping tablespoon of yuca and flatten in palm of hand. Place a cube of cheese in center and pinch the yuca around the cheese to form a ball. Repeat with remaining yuca and cheese.
To fry, heat oil over high heat. Oil should be about 1/2-inch deep.
Add yuca and cook for 1-2 minutes per side, or until golden brown. Remove from oil and drain on paper towels. Serve with guava dipping sauce.
Microwave the guava paste and vinegar until melted and stir until the consistency of barbecue sauce. Add additional vinegar if necessary, to thin.