In a medium bowl, blend the warmed mashed potatoes, 1 beaten egg, parsley, butter, salt and pepper. In a separate bowl, beat the remaining two eggs. Place the flour in a bowl and the bread crumbs in its own bowl.
Working in batches of 10 or so, roll balls of the mashed potato mixture in flour to coat, gently shaking off excess flour. Dip the balls into the egg, let the excess egg drip off and then roll in bread crumbs. Place the balls on a waxed paper covered cookie sheet. Chill, covered, 30 minutes.
Meanwhile, combine the ingredients for the chipotle aioli in a small bowl. Chill.
Preheat oven to 200°F.
Heat 1 1/2 inches oil in a deep heavy pot until it registers 370°F or so. Working in batches, fry croquettes, turning until browned on all sides, about 1-2 minutes per batch. Transfer with a slotted spoon to paper towels to drain, then transfer to a baking pan and keep warm in oven while frying remaining croquettes. (Return oil to 360°F between batches.)
Serve with the dipping sauce.