In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 5 minutes, or until translucent.
Stir in the minced garlic and sliced mushrooms. Cook for an additional 5-7 minutes, until the mushrooms are tender and have released their moisture.
Pour in the chicken broth and bring the mixture to a boil.
Reduce the heat to low and add the shredded rotisserie chicken, heavy cream, dried thyme, salt, and black pepper. Stir well to combine.
Simmer the soup for 10-15 minutes, allowing the flavors to meld together.
Taste and adjust seasoning if necessary. Serve hot, garnished with fresh parsley.