Warm the olive oil in a large Dutch oven over medium heat. Add the onion, carrots, and celery and cook for 6 to 8 minutes, until the vegetables begin to soften.
Stir in the garlic and thyme and cook for 30 seconds, just until fragrant.
Add the rinsed wild rice blend and chicken broth. Bring the soup to a boil, then reduce the heat to low, cover, and simmer for 35 to 40 minutes, until the rice is tender.
Whisk the half-and-half and flour in a bowl until smooth. Slowly stir the mixture into the simmering soup.
Add the shredded chicken, salt, and pepper. Simmer uncovered for 5 minutes, stirring occasionally, until the soup is creamy and slightly thickened.
Taste and adjust the seasoning. Ladle into bowls, sprinkle with parsley if desired, and serve hot.