In a large dutch oven or pot over medium heat, add quartered potatoes and chopped parsnips. Top off with cold water to cover the root vegetables by an inch or so, seasoning water with salt to taste. Bring to a boil and cook for 30 minutes, or the potatoes and parsnips are fork tender. Drain into a colander.
Using a potato ricer (or spaetzle machine, press the potatoes and parsnips into a bowl ; creating a fine purée. If you do not have either device, a potato masher or fork will also work, resulting in a chunkier final product. Warm the milk and butter together in small pan. Add the milk/butter mixture to the potato/parsnip puree and season with salt and pepper.
This side dish goes well with Grand Cru Braised Lamb Shank, Beer Brined Chicken or Wit Braised Chicken.