Place the parsnips in a saucepan, cover with cold water, and bring to a boil. Reduce the heat slightly, cover, and cook until very tender, 20 to 30 minutes. Drain the parsnips and return them to the saucepan. Shake over medium heat for 30 seconds to remove excess moisture. Set them aside.
While the parsnips are cooking, place the potatoes in a saucepan, cover w