You can simply boil the leeks with either of the vegetables, but roasting them adds lots of flavor, especially if you deglaze the pan with lemon juice.
Heat a pot of salted water to a boil.
Heat the oven to 425 degrees.
Peel 1 lb. parsnips and boil, whole, until easily pierced with a knife. Remove from the water and rinse to cool.
Peel 2 lbs. of potatoes (or leave unpeeled) and add to the water. Boil until they are soft. Remove from the pot, reserving the water.
While the root vegetables are cooking, clean and dice 1 leek. Toss in a cast iron skillet or baking dish with 2 T. olive oil and salt. Roast until they are nicely browned but not burnt, 10-15 minutes. Remove from the oven and drizzle with the juice of 1 lemon, then use a wooden spatula to deglaze the pan.
Slice the cooled parsnips in half lengthwise. If they have a tough core, remove it and discard. Roughly chop the tender parts of the roots.
Combine the leeks and lemon juice in a bowl with the root vegetables. Mash, adding salt, pepper and butter (or more olive oil) to taste. If you need more liquid, use a bit of the cooking water. Don’t overmash, or they will be gluey.