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 an additional 5-7 minutes, stirring occasionally, until the mushrooms are tender and have released their moisture.
Pour in the chicken broth and bring the mixture to a simmer. Stir in the shredded rotisserie chicken, dried thyme, and dried rosemary. Season with salt and pepper to taste.
Let the soup simmer for about 10 minutes to allow the flavors to meld.
Reduce the heat to low and stir in the heavy cream, frozen peas, and fresh spinach. Cook for another 5 minutes until the spinach is wilted and the soup is heated through.
Taste and adjust seasoning if necessary. Serve hot, garnished with fresh parsley.