Scoop up some of the mashed potatoes mixture (roughly 3 to 4 tablespoons) and roll a 1-inch by 2 1/2-inch oval football shape. Beat the egg and salt together in a medium bowl. Place the flour in another bowl and the panko bread crumbs in a third bowl.
Roll one of the balls in the flour to coat. Then dunk and roll in the beaten egg. Let any excess egg drip off.
The roll the croquette in the bread crumbs until coated. Place on the baking sheet/plate and repeat with the remaining mashed potato mixture.