My dad, who knew a thing or two about gardening, always said "Wait until the first frosts before digging your parsnips." Well, in recent years, that would pretty much have meant waiting for ever, but this year we've had some real frosts, I sowed some parsnips in the spring (tra-la) and I've dug a few. They are mostly Very Small, which perhaps isn't surprising given the prolonged drought earlier in the year, but I did water them a fair bit.
I suspect that I should also have thinned them out - when I saw that they had germinated, I just didn't have the heart to kill the poor little things. Some were rather piled in together.