Whisk one of the eggs in a small bowl, then add the mashed potatoes and mix thoroughly. Flour your hands a little and shape the potato mix into balls or tubes of whatever size you like. I usually do them on the large side, so make about 8-10. Put the balls on a pan lined with wax paper and refrigerate at least 30 minutes.
Whisk together the second egg in a small bowl. Set out another small bowl of flour and another of bread crumbs. You can use seasoned bread crumbs or panko if you'd like.
Dip the potato balls into flour, then egg, then bread crumbs, covering all sides and set them onto a clean sheet of wax paper.
Heat about 1/2 cup of neutral oil (canola, safflower, etc.) in a frying pan.
Brown each croquette on all sides until crispy, then drain on paper towels.