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In a Dutch oven, add olive oil over medium heat. Add carrots, celery, onion, and garlic, and sauté until tender, about 5 minutes. Add shredded chicken and continue cooking for about 3 minutes, stirring regularly.
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Add broth, heavy cream, and cream cheese, then cover and bring to a boil and let cook for 15 minutes.
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Lower the heat, then add pasta and shredded cheddar cheese and simmer until pasta is almost done. Add spinach and stir until wilted and pasta is fully cooked.
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Top with fresh parmesan cheese and enjoy!