Preheat the oven to 250c. Whisk the eggs in a bowl. Place the flour and breadcrumbs in 2 other bowls.
With your hands, roll 1 rounded tablespoon of the mashed potatoes into a ball. Roll the ball in the flour, eggs and breadcrumbs, and place on a baking sheet. Repeat with the remaining ingredients and refrigerate for 30 minutes.
In a large, deep skillet, heat 1 1/2 inches of olive oil over medium-high heat. When the oil is hot but not smoking, fry the potato balls in batches, turning gently, until golden, about 2 minutes. Remove with a slotted spoon and drain on paper towels. Keep warm on a baking sheet in the oven and fry the remaining croquettes.