Cook a large pot of salted water until boiling, then add ditalini pasta and cook until al dente, about 8-10 minutes. Drain and set aside.

Heat sun-dried tomato oil in a Dutch oven over medium heat. Sauté diced onion, carrots, and celery for 5 minutes until the onion is translucent. Add garlic and cook for an additional 30 seconds.

Incorporate tomato paste and butter into the aromatics, mixing for 1-2 minutes. Add chopped sun-dried tomatoes and sauté for another 2-3 minutes.

Pour in chicken broth, add Italian seasoning, oregano, and basil. Season with salt and pepper, and bring to a boil. Reduce heat and simmer uncovered for 10 minutes.

Stir in shredded chicken, heavy cream, and Parmesan cheese until melted and creamy. Add the reserved pasta and mix gently.

Ladle soup into bowls and garnish with fresh basil if desired. Serve immediately.