In a large heavy-bottomed pot, add the butter, parsnips, carrots, leek, onion, garlic, and celery and cook until just tender and the onions are slightly transparent. Once the vegetables are tender, stir in flour and make sure vegetables are well coated. Add broth, one cup at a time, mixing between additions. Bring to a slight boil and cook while constantly stirring for two minutes. Once the broth has become thick, stir in the heavy cream, parsley, salt, and pepper. Finally, mix in the shredded chicken, set aside, and allow to cool.