Peel and cut potatoes into even chunks and boil in salted water until fork-tender.
Drain the potatoes thoroughly and mash them until smooth with no large lumps remaining.
Stir in the cornstarch, salt, garlic powder, onion powder, and optional cheese until well combined and pliable.
Roll the mixture into golf-ball-sized portions.
Dip each ball into the beaten eggs, then roll in panko breadcrumbs until evenly coated.
Heat oil in a deep pot to 350°F and fry the balls in batches until golden brown and crispy.
Remove with a slotted spoon and drain on a wire rack or paper towels before serving.