In a Dutch oven, melt the butter over medium heat and saute the onion and celery until tender, about 5 minutes. Do not let the onion brown. Stir in the parsnips and potatoes. Pour the chicken stock over the vegetables and bring to a boil. Reduce the heat to low and simmer for 20 minutes, or until the vegetables are tender.

Remove from the heat and use an immersion blender to puree the soup. Or transfer it to a blender and puree in batches. Wipe out the Dutch oven and return the soup. Stir in the half and half, salt, and pepper to taste; cook over low heat for another 7 minutes, or until steaming.

Ladle into soup bowls and serve with a swirl of cream, garnish with chives.