Peel the potatoes and cut them into small dice, about 3/4 inch and certainly no larger than 1 inch. Rinse the diced potatoes in hot water, drain well, and dry them thoroughly with a clean cloth or paper towels--this seems to prevent the potatoes from sticking together during cooking.
In a very large, heavy-bottomed skillet, heat the oil and butter. Add the potatoes--the pan should be large enough to take them very comfortably more or less in a single layer, otherwise use 2 pans.
Season liberally with salt and pepper. Over a low heat saute the potatoes until crisp and golden; this may take up to 1 hour. Turn the heat down if the potatoes are browning too much. Stir frequently with a wooden spatula and give the pan an occasional good shake. Snip the parsley into a bowl and add the potatoes. They won't need draining, but if they look even remotely greasy, drain them on paper towels. Check the seasoning, and sprinkle the potatoes with extra snipped parsley. Serve hot.
Recipe courtesy of CUISINE GRAND-MERE (Time-Life Books) by Marie-Pierre Moine