Cover potatoes with cold, salted water in a large pot and bring to a boil; boil for 5 minutes. Add parsnips and boil until vegetables are cooked through, 15 to 20 minutes. Drain and return to pot.
Shake pot over low heat to dry vegetables slightly. Add butter, cream, salt, pepper and, if desired, nutmeg. Mash with a potato masher to desired consistency. Sprinkle with parsley, if desired, and serve hot.