To a large Dutch oven or a pot on the stove over medium heat to add in the oil. Once the oil is hot, add in the minced garlic, onion, and carrots cook together for 5 to 7 minutes to soften the vegetables.
Add in the cooked shredded chicken, broth, heavy cream, and cream cheese stir will cover with a lid and turn the heat to low. Let simmer for five minutes then whisk well to help melt the cream cheese down and incorporate it in.
Add in the pasta and spinach stir well, cover with a lid and let it simmer on the stove for 10 minutes or until the pasta is tender (while simmering stir occasionally so the pasta doesn’t stick).
Stir in the cheddar cheese, and Parmesan cheese. Once the cheese melts down, you can serve.