Add the sundried tomato oil to a large Dutch oven or pot and heat over medium heat. Add the onion, carrots, and celery and saute for 5 minutes, stirring occasionally. Add the garlic and saute another 30 seconds.
Add the tomato paste and butter. Once the butter is melted, stir until the veggies are evenly coated with the tomato paste. Add the sun-dried tomatoes and saute for 2-3 minutes.
Stir in the chicken broth and seasonings, and bring to a boil. Once boiling, reduce to a simmer and simmer for 10 minutes.
Carefully drop the shelf-stable gnocchi into the pot while simmering, and continue to cook for 2-3 minutes, or until the gnocchi float to the top. Remove from heat.
Stir in the shredded chicken, heavy cream, and Parmesan cheese. Stir until the cheese is melted and everything is heated through. Serve garnished with fresh basil if desired!