In a large Dutch oven, heat 1–2 tbsp oil over medium-high heat. Sear the chicken breasts on both sides until a nice crust develops, then remove from the pan. The chicken doesn’t need to be fully cooked.
In the same pan, reduce heat to medium. Add in a touch of sun-dried tomato oil from the jar and sauté the onion, celery, and carrot with salt, pepper, Italian seasoning, and smoked paprika for a few minutes.
Once soft, add in the garlic, sun-dried tomatoes, and Calabrian chili paste and stir. Clear a center in the pot and add in the tomato paste. Let it caramelize in the pan for 1–2 minutes before stirring with the rest.
Deglaze with the white wine, scraping up any brown bits on the bottom of the pan. Let that simmer for another minute.
Pour in the chicken broth and season with salt and pepper.
Add the chicken back into the pot along with a Parmesan rind. Bring to a boil, then reduce heat to low. Cover and simmer for 10–12 minutes, then remove the chicken and Parmesan rind from the pot. Shred the chicken and set aside.
Pour in the room temperature heavy cream and stir. Add in the gnocchi and cooked chicken. Simmer for a few minutes until the gnocchi is tender.
Finish the soup with spinach, basil, and Parmesan. Stir to wilt the spinach, taste for seasonings and enjoy!
