1Combine potatoes and enough water to cover in a large saucepan. Cook over medium-high heat until potatoes are tender, about 20 to 25 minutes; drain. Beat potatoes until slightly cooled.
Beat 2 eggs in a small bowl. Add to potato mixture and mix well. Stir in Parmesan, parsley and salt. Shape into 15 (3-inch) patties.
Combine remaining eggs and the water in a small bowl and mix well.
Coat potato patties with flour, then dip in egg mixture. Coat with bread crumbs. Arrange in a single layer on a baking sheet. Chill, covered, for 1 hour.
Preheat the oven to 275ºF.
Preheat vegetable oil in a deep fryer. Deep-fry potato patties in hot oil until golden, about 3 minutes; drain on paper towels. Remove to a baking sheet. Bake for 10 minutes. Serve with spicy mustard, if desired.