Cook wild rice in 4 cups (960ml) of water for 45 minutes or until it fluffs up. Drain any remaining liquid left in the pot. Set aside.
In a large pot, add vegetable oil. Sauté onions, carrots, and celery until soften, about 3 minutes. Add dried thyme and all-purpose flour. Cook and stir for another 2 to 3 minutes.
Pour in chicken stock. Bring to a boil.
Add cooked chicken, mushrooms, salt, and pepper. Reduce heat and allow soup to simmer for 10 minutes.
Add cooked wild rice and pour in half-and-half. Bring soup back up to a boil and allow it to heat through, about 5 minutes.
Turn off heat. Stir in chopped parsley.