Fill a deep frying pan with oil, about 1 inch deep, and heat over high heat. Add the potatoes, reduce heat to medium/high and cook until tender (about 20 minutes). Stir once after about 10 minutes.
Break the eggs in a bowl, add a pinch of salt, freshly grated black pepper, the parsley (if using), and a splash of water. Beat well with a fork until homogenized.
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