Place a flameproof casserole with cold water over medium heat. When the water reaches a boil, add coarse salt to taste; then add the potatoes and simmer until the potatoes are soft (about 35 minutes for medium potatoes).
Meanwhile, finely chop first the garlic, then the parsley. Place them in a serving bowl, along with the olive oil and salt and freshly ground pepper to taste.
When the potatoes are ready, peel them while still very hot and cut them into pieces about 1 inch square. Add the potato pieces to the bowl and mix with the other ingredients, using a wooden spoon.