Peel the yucca root thoroughly, removing both the waxy outer layer and pinkish layer underneath. Cut into 2-inch chunks.
Bring a large pot of salted water to a rolling boil. Add yucca chunks and cook for 20-25 minutes until fork-tender.
Drain well and let cool slightly. Cut each chunk in half lengthwise and remove the tough fibrous core from the center.
Mash the yucca with a fork or potato masher until you achieve a smooth yucca puree consistency.
Transfer mashed yucca to a large bowl. Add beaten egg and flour. Mix until the mixture holds its shape when pressed.
Shape the mixture into round yuca patties, about 3 inches wide and 1/2 inch thick. You should get 12-14 yucca cakes.
Heat vegetable oil in a large skillet over medium-high heat (about 1/4 inch deep). Fry yucca cakes in batches for 3-4 minutes per side until golden brown and crispy.
Transfer to paper towel-lined plate to drain. Sprinkle with sea salt while still hot.
For the garlic mojo: Heat olive oil in a small saucepan over medium heat. Add minced garlic and cook for 30 seconds until fragrant.
Remove from heat. Stir in lime juice, white vinegar, cumin, and black pepper. Add chopped cilantro. Taste and adjust seasoning.
Serve yucca cakes immediately with garlic-lime mojo drizzled on top or on the side for dipping.