Take a large saucepan, put the potatoes, cover with cold water and bring to boil. Cook until softened.Drain and peel while the potatoes are hot . Then push them through the food mill with large holes several times. You can use a ricer. Mix and blend them until smooth.
Add the butter, Parmesan and Parsley. Then season with salt and pepper. Gradually blend in the egg yolks, one at a time.
Shape croquettes.
Put some flour on a plate. Put egg whites in a bowl, and whisk until foaming. Put the breadcrumbs on another plate.
Dip each croquette in the flour until coated all over, then dip it into the egg whites, and finally coat in the breadcrumbs.
Heat the oil in a large pan to 180 C/ 350 F or until a small cube of bread browns in 40 seconds.
Fry the croquettes until crisp and golden.
Serve piping hot.