Peel the potatoes and cut into quarters. Put into a pan with the basil leaves and lemon zest. Cover with water. Bring to a boil, cover the pan and reduce the heat.Simmer about 15 to 20 minutes, or until the potatoes are tender.
Drain the potatoes in a colander. Discard the basil and lemon peel. Put into a large bowl and add the olive oil, green olives and salt. Using an electric mixer or potato masher, mash the potatoes coarsely. Serve hot.