It's a shame when the sweet taste and creamy texture of parsnips is ruined by stringy fibers. To avoid this problem, choose thin, young parsnips, rather than the thicker, older parsnips that are likely to have a woody center, Bacardi1 says. If older parsnips are all you have and you don't mind serving puréed parsnips (as in this parsnip and cauliflower recipe), consider running your cooked parsnips through a food mill, greygarious says. Puréeing has drawbacks, though; Robin Joy notes that there's nothing quite like the "slightly caramelized, chewy, browned fingers of parsnip from around a roast chicken/piece of meat."
Photograph of CHOW's Potato and Parsnip Mash by Chris Rochelle / CHOW.com