Quarter potatoes. Put potatoes and 2 tablespoons salt in a large pot and cover with cold water by 1 inch. Bring to a boil, covered with lid, then reduce heat and simmer, partially covered, until potatoes are very tender.
Reserve 1 cup cooking water, then drain potatoes in a colander and return to pot. Add oil, pepper, remaining 1 teaspoon salt, and 1/2 cup cooking water and mash with a potato masher or fork. Add more cooking water for a looser consistency.
Makes 8 servings