In a deep bowl, combine the yams, butter, onion, parsley, salt and a liberal grinding of pepper, and knead until the mixture is fairly smooth and thick enough to come away from the sides of the bowl in an almost solid mass.
Line a large shallow baking dish with paper towels and place it in the oven. Preheat the oven to the lowest setting. In a heavy 10- to 12-inch skillet, heat the oil over moderate heat until a light haze forms above it. For each cake, drop about a tablespoon of yam mixture into the hot oil. Cook 4 or 5 at a time, leaving space between them so they can spread into 2- to 2 ½-inch rounds. Fry the cakes for about 4 minutes on each side, or until golden-brown and crisp around the edges. As they brown, transfer the frituras de name to the lined dish to drain and keep warm. Serve at once.