In a large Dutch oven, pour oil to a depth of 2 inches; heat over medium heat until a deep-fry thermometer registers 340°.
In a large bowl, stir together mashed potatoes, 1 egg, chives, salt, and pepper. In a shallow bowl, place flour. In another shallow bowl, whisk together remaining 2 eggs and 1 tablespoon water. In a third shallow bowl, place bread crumbs.
Form potato mixture into 8 (2½-inch-wide) patties (¼ cup each). Dredge each patty in flour, shaking off excess. Dip in egg wash and then roll in bread crumbs to coat.
Working with 2 patties at a time, deep-fry until golden brown on all sides, about 2 minutes. Let drain on a wire rack. Serve warm. Garnish with chives, if desired.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/mashed-potato-croquette/