Cook the whole potatoes in salted cold water: bring to a boil, then simmer gently 15-20 minutes until fork-tender.
Cool slightly, peel, transfer to a bowl, and mash until smooth and lump-free.
Add the cornstarch, Parmesan, parsley, salt, and pepper; mix thoroughly and adjust seasoning.
Roll small portions into uniform balls between your palms.
Heat frying oil to about 350F (175C), hot but not smoking.
Carefully lower the potato balls into the oil without crowding, frying in batches if needed. Fry 3-4 minutes until golden brown and crispy, turning occasionally.
Transfer to a paper towel-lined plate with a slotted spoon to drain.
Serve immediately while hot and crispy, with a dipping sauce if you like.
