In a medium bowl, combine the mashed potatoes, shallots, garlic cloves, egg, and Italian parsley. Shape into 1 inch balls.
Refrigerate the potato balls for 30 minutes.
Next, roll the potato balls in the parmesan cheese and breadcrumbs. Preheat a skillet with about 2 inches of oil on moderate heat.
Fry potato balls on all sides, a few at a time, for 2-4 minutes or until golden brown. Remove with a slotted spoon to paper towels to drain. Serve immediately.