1. Heat the butter and olive oil in a large soup pot over medium heat. Add the onion, carrots, and celery, then cook for 4 to 5 minutes until softened.

2. Stir in the garlic and sliced mushrooms. Cook for 8 to 10 minutes, stirring occasionally, until the mushrooms release their moisture and begin to brown.

3. Sprinkle the flour over the vegetables and stir well to coat everything evenly. Cook for 1 minute.

4. Slowly pour in the chicken broth while stirring to keep the soup smooth.

5. Add the dried thyme, dried parsley, salt, black pepper, and crushed red pepper flakes. Bring the soup to a gentle simmer and cook for 10 minutes.

6. Stir in the shredded rotisserie chicken, heavy cream, and whole milk. Reduce the heat to low and cook for 5 to 7 minutes until the chicken is heated through and the soup is creamy.

7. Taste and adjust seasoning if needed. Ladle into bowls and top with fresh parsley and Parmesan cheese if desired.