Heat olive oil in a large pot over medium heat. Add diced onion, carrots, and celery. Sauté for about 5 minutes, or until the vegetables become tender and the onion is translucent.
Add minced garlic, dried thyme, and dried rosemary to the pot. Stir and cook for an additional 1-2 minutes until fragrant.
Pour in the chicken broth and bring to a boil. Once boiling, add the shredded chicken and gnocchi. Cook for about 3-5 minutes, or until the gnocchi floats to the top.
Reduce the heat to low and stir in the fresh spinach and heavy cream. Cook for another 3-5 minutes until the spinach wilts and the soup is heated through.
Season with salt and pepper to taste. Adjust the seasoning as needed.
Serve the soup hot, garnished with grated Parmesan cheese if desired.
For added convenience, consider using rotisserie chicken instead of cooking chicken from scratch.
If looking for a lighter version, substitute heavy cream with half-and-half or milk.