Rinse wild rice under cold water to remove excess starch, then combine it with chicken broth in a medium saucepan. Bring to a boil, reduce heat to low, cover, and simmer for 45-50 minutes. Drain excess liquid and set aside.

In a large pot, heat olive oil over medium heat. Add chopped onion, diced carrots, and celery. Sauté for 5-7 minutes until softened and onions are translucent. Stir in sliced mushrooms and cook for an additional 3-4 minutes. Add minced garlic, thyme, sage, and rosemary, cooking until fragrant.

Pour in remaining chicken broth, add cooked wild rice and shredded chicken. Stir and simmer over medium heat, then reduce to low, cover, and let flavors meld for 30-60 minutes.

Stir in heavy cream or coconut milk, and dry sherry if using. Add chopped parsley and season with salt and pepper to taste. Heat until warm, avoiding boiling.

Ladle soup into bowls and garnish with toasted nuts and grated cheese if desired.