Cut them in chunks. It could take anywhere from 15-30 minutes, depending on the thickness and age of the roots. When you cut them up, slice through a thick piece the long way, and look at the core inside. Occasionally, it can be very 'woody' if the parsnip is old. If you find that, cut it out. A woody core won't mash nicely.
My favorite way to make them is to puree them with a splash of heavy cream. Then set them in a bowl over a pan of simmering water (like a double boiler) while you make the rest of the meal. They mellow during this 15-30 minute rest and become sweeter. (An old Julia Childs trick).