In a large pot or dutch oven, melt the butter over medium heat. Add the carrots, celery, shallots, and mushrooms, and sprinkle with salt and pepper. Cook for 2-3 minutes, until fragrant. Add the garlic and cook for another 2 minutes. Stir in the broth, chicken, thyme, sage, and wild rice, and season with salt and pepper.
Bring to a boil over high heat. Once boiling, reduce the heat to low and cover. Cook 40-50 minutes or until the rice is tender and the chicken can be shredded with a fork.
Shred the chicken with two forks. Stir in the cream and cook over medium heat until warmed through, about 10 minutes.
Meanwhile make the parmesan toast. Preheat the oven to 425 degrees F.
Melt the butter and stir in the herbs. Using a pastry brush, brush the butter mixture onto the slices of bread. Lay the slices of bread on a baking sheet and sprinkle with parmesan cheese. Bake for 10-15 minutes or until toasted. Once ready to serve the soup, stir in the parsley, sprinkle with parmesan cheese and a piece of parmesan herb toast.
After cooling, keep the soup in an airtight container for 4 days. When reheating, add some broth as the rice will soak up some of the liquid.