Place the peeled and cubed potatoes in a large pot and cover them with cold water. Season generously with salt and bring to a boil over high heat. Reduce to a simmer and cook until the potatoes are fork-tender, about 15 to 18 minutes. Drain well.

Transfer the potatoes to a large mixing bowl and mash until smooth. Stir in the salt, pepper, and parsley. Sprinkle in the cornstarch and mix until evenly combined. The mixture should be firm enough to hold its shape when rolled.

Using your hands or a small cookie scoop, form the potato mixture into bite-sized balls, about the size of a walnut. Arrange them on a parchment-lined tray.

Heat the vegetable oil in a deep fryer or heavy-bottomed pot to 350°F (175°C). Working in batches, gently lower the potato balls into the hot oil and fry until golden brown and crispy, about 4 to 5 minutes. Use a slotted spoon to transfer them to a paper towel–lined plate.

Serve hot with ketchup or your favorite dipping sauce.