Put a pan of salted water on to boil. Add the unpeeled potatoes and boil, covered, for about 20 minutes, or until they are soft, and completely cooked through.
Preheat the oven to 350 degrees.
Drain the potatoes and , when are cool enough, peel them. Mash them well in a wide bowl. Add the beef, parmesan, egg, and salt, and mix thoroughly with your hands.
Roll into balls about the size of small walnuts and then flatten them a bit into little ovals.
Put the bread crumbs on a plate and pat the croquettes in them to coat both sides. Drizzle about 2 1/2 tablespoons of oil over the bottom of a large baking pan, spreading it around witht the back of a spoon.
Pack the croquettes like tight soldiers on the pan and drizzle lightly with another couple of tablespoons of oil.
Put the pan in the oven and bake the croquettes for about 30 minutes, or until the undersides are nicely golden and a bit crisp. Turn them over gently and bake for another 10 minutes, or longer if necessary, until the new undersides become nicely golden,
Serve warm or at room temperature with a small scattering of salt, if you think they need it.