Boil potatoes whole until completely tender, peel while warm, and mash smoothly.
Gradually fold all-purpose flour and salt into the warm mashed potatoes to form a soft, workable dough without over-kneading.
Roll dough into long ropes, cut into small pillow shapes, and indent with a fork.
Drop gnocchi into boiling salted water; remove with a slotted spoon as soon as they float to the surface (about 2 minutes).
Toss cooked gnocchi in melted butter, black pepper, and grated parmesan cheese before serving.