Combine the potatoes in a large pot of water. Cover and bring the water to a boil. Continue boiling until the potatoes are tender, about 15 minutes. Drain, reserving 3/4 cup of the cooking liquid. Return the potatoes to the pot. Coarsely mash the potatoes, adding enough reserved cooking liquid to moisten. Using a large fork, stir in the Parmesan and the oil. Season the potatoes, to taste, with salt and pepper and serve.