Mix the mashed potatoes, egg, parsley, salt, and pepper until well combined.
Place the flour, beaten egg and breadcrumbs in three separate trays or bowls.
Take a handful of potato mixture, shaping into a log shape or ball, and dip into flour, then egg and then breadcrumbs; repeat (yes, do it twice, it's worth it!) I love these stainless steel trays for dipping.
Place on a plate or tray (dusted with cornmeal or breadcrumbs) and refrigerate for about an hour.
When ready to cook/eat, heat oil in a small pot, over medium high heat, so that the croquettes may be deep fried.
Fry two or three at a time, depending on how many fit, carefully turning (with tongs) once, until evenly browned. Remove, and place on towel-lined plate to cool a little.
Continue with the rest of the potato mixture until it is all finished. You can keep the first ones hot in the oven, until the rest are done. Serve hot, on their own with HP Sauce, or as a side.