Heat the olive oil in a large soup pot or Dutch oven over medium-high heat. Add the chicken, 1 teaspoon of Italian seasoning, salt, and pepper to taste. Cook until browned on all sides, about 4 to 5 minutes.
In the same pot, add the onions, carrots, celery, sun-dried tomatoes, and garlic. Cook until the vegetables are translucent, about 3 to 4 minutes.
Sprinkle the flour evenly over the mixture and stir well to combine. Add the flour in stages to prevent drying out. If using tomato paste, add it now and stir to incorporate.
Gradually whisk in the chicken broth, stirring consistently to avoid lumps. Use your spoon to deglaze the bottom of the pan by scraping up any browned bits.
Bring the mixture to a rolling boil, then add the pasta, 1 teaspoon of Italian seasoning, salt, and pepper to taste. Cover with a lid and reduce the heat to low. Let the soup simmer for about 20 minutes, or until the chicken is cooked through and tender and the pasta is al dente. Alternatively, you may cook the pasta separately and add it later.
Remove the lid and stir in the heavy cream, fresh spinach, and grated Parmesan cheese. Let the soup simmer for another 5 minutes.
Taste and adjust the seasoning with salt and pepper as needed before serving.