Heat olive oil in a large pot or Dutch oven over medium heat. Add the diced chicken and cook until browned and cooked through, about 5-7 minutes. Remove the chicken and set it aside.
In the same pot, add the chopped onion and cook for about 3 minutes until softened. Stir in the minced garlic and cook for another 1 minute until fragrant.
Add the sliced mushrooms, diced carrots, and diced celery to the pot. Cook for 4-5 minutes until the vegetables are tender.
Pour in the chicken broth and Marsala wine. Stir in the dried thyme, salt, and black pepper. Bring the mixture to a boil.
Once boiling, reduce the heat to low and add the gnocchi. Allow the soup to simmer for about 5 minutes or until the gnocchi are cooked through.
Stir in the heavy cream and Parmesan cheese, mixing well. Let the soup simmer for an additional 3-4 minutes until heated through.
Return the cooked chicken to the pot and mix to combine. Cook for another minute. Adjust seasoning with salt and pepper if needed.
Serve the soup hot, garnished with fresh parsley if desired.