Wash and peel the potatoes and cut them into equal sized chunks.
Cover them with cold water and bring to a boil.
Add salt and boil until a butter knife pierces through easily.
Strain all water and mash.
Set apart 2 heaping cups of the potato puree for the recipe.
Make the bechamel sauce by first melting the 8 T of butter on a medium heat in a heavy saucepan.
Once it is melted, slowly add in the flour, always stirring so that it doesn't stick.
Stir constantly for about 5 minutes to completely cook the flour.
Finally, add the milk and cream, a little at a time, alternating between additions over about a half an hour, constantly stirring.
When you have a creamy bechamel without any lumps, add the mashed potato (which should still be hot) and a pinch of salt.
Using either a hand blender or a countertop blender, blend the sauce while adding the cubed butter.
When the mixture is smooth, let it cool completely, for at least 4 hours in the refrigerator (or to speed this up spread it on a cookie sheet, covered with clingfilm).
Finally, form the croquettes with your hands and dip them in beaten egg followed by breadcrumbs.
Let the formed croquettes rest in the fridge for another hour or so before frying them for best results (they could also be frozen at this point).
Fry the croquettes in hot olive oil (if possible) or vegetable oil/sunflower oil if not.
Let the potato croquettes rest on paper towels and serve hot with dipping sauces if desired.