In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 3-4 minutes until translucent.
Add the minced garlic and sliced mushrooms to the pot. Cook for another 5-7 minutes until the mushrooms are tender and have released their moisture.
Pour in the chicken broth and add the diced carrots, celery, shredded rotisserie chicken, thyme, and rosemary. Bring the mixture to a boil, then reduce the heat and let it simmer for 15-20 minutes.
Stir in the heavy cream and season with salt and pepper to taste. Allow the soup to heat through for an additional 5 minutes.
Serve hot, garnished with fresh parsley.