In a large dutch oven, heat olive oil over medium-high heat. Once hot, add diced onion and cook for 5 minutes. Roughly chop sun-dried tomatoes and add them to the onions, along with their oil. Cook for another 2-3 minutes and then add in garlic, and cook for another minute.
Stir in tomato paste, basil, Italian seasoning, red pepper flake, salt, and pepper.
Add chicken breasts to top of saute mixture and then immediately add broth. Bring to a boil. Once boiling, cook chicken breasts for 12 minutes or until 160F. Take chicken breasts out and place on a separate plate.
Add chunks of cream cheese to pot, along with whole milk, vinegar, and parmesan cheese. Use a whisk to help break up the cream cheese as it warms until it is smooth. Let simmer for a few minutes.
While simmering, shred chicken or cut into small bite sized pieces.
Add chicken back into the soup, and then add the gnocchi and pasta in. Bring to a boil. Once boiling, cook for 12 minutes, stirring often. Add in the spinach, and let soup simmer for 20 minutes on medium-low heat, stirring occasionally.
Top with more fresh basil and parmesan cheese. Enjoy!