1. Heat the olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Add the cubed chicken breast and cook until lightly browned on all sides and cooked through, about 5-7 minutes. Remove the chicken from the pot and set aside on a plate.

2. Reduce the heat to medium. Add the chopped onion, sliced mushrooms, celery, and carrots to the pot. Cook, stirring occasionally, until the vegetables begin to soften, about 8-10 minutes.

3. Stir in the minced garlic, dried thyme, and dried rosemary. Cook for another minute until fragrant, being careful not to burn the garlic.

4. Sprinkle the flour over the cooked vegetables and stir constantly for 1-2 minutes. Gradually whisk in the chicken broth, making sure to scrape up any browned bits from the bottom of the pot. Bring the mixture to a simmer.

5. Add the uncooked wild rice blend to the simmering broth. Reduce the heat to low, cover the pot, and let it simmer for about 15-20 minutes, or until the wild rice is tender. Check the package directions for your specific wild rice blend, as cooking times can vary.

6. Once the wild rice is tender, stir in the milk and heavy cream. Return the cooked chicken to the pot. Continue to simmer gently for another 5-7 minutes, or until the soup is heated through and slightly thickened to your desired consistency. Do not let the soup come to a rolling boil after adding the dairy, as it can curdle.

7. Taste the soup and season generously with salt and freshly ground black pepper. Ladle the hot soup into bowls, garnish with fresh chopped parsley, and serve immediately.