Select the smallest potatoes possible, about the size of golf balls, about three per person. Scrub them well. Quarter them but do not peel them (if they are larger size, you may have to cut them in eighths). Heat butter and cooking oil to a depth of one-half inch in a large, heavy skillet.
Add potatoes and cook over medium-high heat until they begin to brown. Lower heat, cover skillet and continue cooking potatoes for about 20 minutes, until they are tender, stirring them from time to time.
Uncover the skillet, increase heat and rapidly finish browning the potatoes. Drain them well, sprinkle them generously with salt and freshly ground pepper and chopped parsley and serve.