Sweat out leeks, thyme, and shallots in 4 T butter. Season with salt and pepper.Peel and dice parsnips. When leeks and shallots are soft, add the parsnips, salt and pepper. Cook gently until parsnips are soft and cooked through, being careful that nothing browns.
Add a mixture of cream and 1/2 chicken stock and 1/2 water - enough to cover above parsnips etc by about 2 inches. Be sure to use a pot that is wide enough to allow the parsnips to cook in one flat layer and tall enough to accommodate the chicken stock, water, and cream. Add more salt and pepper. Cook over high heat until soup comes to a boil. Puree in batches with the remaining 4 T butter.
Season to taste. Pass through a strainer.