In a large pot, heat the olive oil over medium heat. Add the diced onion, garlic, carrot, and celery. Sauté for about 5 minutes, until the vegetables are softened.
Stir in the dried oregano, basil, and red pepper flakes (if using). Cook for an additional minute until fragrant.
Add the diced chicken to the pot and cook until no longer pink, about 5-7 minutes.
Pour in the chicken broth and diced tomatoes. Bring the mixture to a boil, then reduce the heat and let it simmer for 15 minutes.
Stir in the heavy cream and fresh spinach. Cook for another 5 minutes until the spinach is wilted. Season with salt and pepper to taste.
Serve hot, topped with grated Parmesan cheese and chopped parsley.