Heat a large Dutch oven or heavy bottom saucepan over medium-high heat. Cook the bacon until crisp and remove to a paper towel lined plate to drain. Chop bacon and set aside. Remove all but 1 tablespoon of the bacon grease from the pan.
Add the onion, carrots and celery to the pan and sauté in the drippings for 3-4 minutes on medium-high heat. Add the thyme leaves, mushrooms, and garlic. Sauté for 5 minutes or until the mushrooms release their moisture and start to brown.
Add the chicken broth, wine (or water) and bring to a boil. Reduce the heat and simmer for 10 minutes or until the vegetables are crisp tender. Add the salt, pepper, chicken and cooked wild rice. Stir gently.
In a small bowl with a spout, whisk together the half-and-half with the flour until smooth. Slowly drizzle the flour mixture into the hot soup while stirring gently to combine. Allow the soup to cook for about 5 minutes or until thickened.
Add the spinach and stir to wilt. Top with chopped bacon and serve.