In a large pot or Dutch oven, heat the 2 tablespoons of butter and 1 tablespoon of olive oil over medium heat. Once the butter has melted, add the 4 smashed cloves of garlic and the 1/2 chopped sweet onion. Sauté for about 3-4 minutes, or until the onion becomes translucent and fragrant.
Add the 6 ounces of sliced cremini mushrooms and 2 ounces of wild mushrooms to the pot. Sauté for another 5-7 minutes until the mushrooms are softened and begin to release their juices.
Sprinkle in a pinch of kosher salt and freshly cracked pepper to taste, along with 1 tablespoon of fresh chopped thyme. Stir everything together and let the flavors meld for another minute.
Pour in the 6 cups of low sodium chicken broth and bring the mixture to a gentle boil. Once boiling, add in the 1 cup of wild rice. Lower the heat to a simmer, cover the pot, and let it cook for about 45-50 minutes, or until the rice is tender.
While the rice is cooking, season the 1/2 - 1 pound of boneless skinless chicken breasts or tenders with salt and pepper. In a separate skillet, cook the chicken over medium heat until it's fully cooked through, about 6-7 minutes per side depending on thickness.
Once the wild rice is tender, add the cooked chicken pieces back into the soup. Stir in 1 cup of whole milk and 1/2 cup of grated parmesan cheese, allowing the cheese to melt into the soup.
Ladle the Cream of Mushroom Chicken Wild Rice Soup into bowls and garnish with additional thyme or parmesan if desired. Serve hot and enjoy!