Our favorite way to eat them is well washed, rolled in a little sea salt, and eaten raw with the tops still attached. My boys gobble them up this way like they are the best thing in the world, and they prefer them to fresh carrots most of the time. It is a highlight of our short winter days heading out to the parsnip patch to grab a snack.
They do have to be fairly small/young though- mine are best when less than an inch across the top.
My parsnips were all eaten by deer this year just as they started to take off. What a shame!