Boil potatoes until tender, then mash in a bowl.
Add grated cheese, chopped green onions, salt, and pepper to the mashed potatoes and mix well.
In a separate bowl, beat the egg.
Form small balls from the potato mixture, about 1 inch in diameter.
Dip each ball in the beaten egg, then roll in breadcrumbs to coat.
Heat oil in a frying pan over medium heat.
Fry the potato balls in batches until golden brown, about 3-4 minutes.
Remove from oil and place on paper towels to drain excess oil.