Good morning Richard and thank you for reaching out to ask2.extension. 
parsnips grow best in soil that is amended to be loosely packed, so I think you need some soil for them to grow.  I don’t grow them so I don’t have any first hand knowledge.  I found the following information from the Farmer’s Almanac.

Parsnips need a long growing season and are best harvested after a few fall frosts; if planted too late in the season, their roots will be small.
Water in summer if rainfall is less than 1 inch per week. Parsnips need a fair amount of moisture to form healthy roots.

As long as you started with good soil, fertilizing is likely not necessary. Excess nitrogen will encourage top growth instead of root growth.

Once roots start to form, hill soil around the plants’ base to prevent greening of the roots’ shoulders.

Poor Parsnip Plant Companions:  Carrots, Celery, Dill and Fennel.

For the rest of the summer I would be sure to give them plenty of water, especially since you compost probably drains really well and no fertilizer.

I hope this helps.

Some plants just need that real dirt!  Compost is great, but sometimes it is the nutrients in real dirt.  So maybe next year consider mixing in some black dirt with your compost.

If you go to Extension.umn.edu and search  soil testing, choose the article test your soil this spring and click on the red University of Mn soil testing lab it will give you where to send the sample and how to do it.

I still believe our hot dry summer has a lot to do with a lot of issues people are having this year.