Heat the oven to 400°F. Rub chicken with olive oil, 1/2 teaspoon salt and pepper and place skin-side up in a small roasting pan. Roast for 35 to 45 minutes, or until the thickest breast meat reaches 165°F, then rest for 10 minutes.
Meanwhile, bring rice water to a boil in a saucepan. Add wild rice, cover and simmer gently for 45 to 55 minutes until tender and many grains have split; drain any remaining water.
Melt butter in a soup pot over medium heat. Cook leeks for 7 minutes, then add parsnips, broth, thyme and remaining salt. Cover partly and simmer for 20 to 25 minutes until parsnips are soft.
Remove chicken skin and bones and discard them. Shred the meat into short pieces, retaining the clear roasting juices.
Blend the parsnip and leek broth until smooth with an immersion blender. Fold in cooked wild rice, shredded chicken and roasting juices.
Add cream and heat gently for 5 minutes until steaming throughout without a hard boil. Divide among 6 bowls.