Boil the Potatoes: Peel the potatoes, cut into large chunks, and place in a pot of salted boiling water for 12 to 15 minutes until completely tender when pierced with a fork.
Drain and Mash: Drain the potatoes well in a colander, then transfer to a large bowl and mash until completely smooth and dry, without adding any milk or butter.
Season the Mixture: Let cool slightly, then add the cornstarch, garlic powder, paprika, black pepper, salt, and fresh parsley, mixing thoroughly until you have a soft, pliable potato dough.
Form the Cone: Take a portion of potato mixture about the size of a small clementine, flatten it gently, place a cube of mozzarella in the center, and seal the potato around the cheese by gently pulling and shaping the mixture upward into a cone or ball.
Optional Freezing: Place the formed cones on a parchment-lined tray and freeze for 15 to 20 minutes before frying to help them hold their shape.
Heat the Oil: Pour enough oil into a large skillet to come at least halfway up the height of the cones, then heat over medium heat until the oil shimmers gently.
Fry Until Golden: Carefully place the cones into the hot oil and fry for 2 to 3 minutes on each side, turning gently with a slotted spoon, until evenly golden brown.
Drain Excess Oil: Transfer the fried cones to a paper towel-lined plate immediately after frying to remove excess oil and keep them crispy.
Serve Hot: Arrange the cones on a serving platter and serve while still hot and the cheese inside is warm and gooey.