Heat olive oil in a large soup pot over medium heat. Sauté the chopped onion for 3 to 4 minutes until softened and translucent.
Add garlic and carrots, cooking for another 2 to 3 minutes until fragrant.
Stir in the sliced mushrooms and cook for 5 to 7 minutes until they release moisture and begin to brown.
Add the shredded rotisserie chicken and soy sauce. Stir and cook for 2 to 3 more minutes.
Pour in the chicken broth and water. Stir in dried thyme, rosemary, salt, and pepper. Bring the soup to a gentle simmer and cook for 10 minutes.
In a small bowl, whisk the flour with a few tablespoons of water to create a slurry. Slowly pour it into the soup, stirring constantly to avoid lumps.
Add heavy cream and the butter. Let the soup simmer gently for another 5 minutes, stirring occasionally until slightly thickened.
Taste and adjust seasonings as needed.
Serve hot, garnished with fresh parsley, a side of crusty bread, or a sprinkle of Parmesan if desired.