Cut the yuca lengthwise into 1-inch pieces. They will be half-moon-shaped chunks, since yuca is a cylindrical vegetable and is usually cut in long, half-cylinders. Remove the center stem.
In a small stockpot place the yuca and 3teaspoons of salt, and cover completely with water. Simmer over medium heat until the yuca is so soft that you can insert a knife smoothly into it—about 20 minutes for good yuca. It should feel like a potato when done.
Remove the yuca from the water. Sprinkle with the remaining ¼teaspoon of salt and mash with a potato masher or pass through a molino* (corn mill).
Form balls of about 1tablespoon of mashed yuca.
Pour the oil into a deep, medium, heavy pot, and place over medium-high heat. When the oil is hot (about 350°F), add the yuca balls and deep fry for 2 minutes. Remove them with a slotted spoon and drain on paper towels. Let cool for 2 to 3 minutes to set the shape.
Place on a serving dish and pour the Melado over them. Enjoy!