Using a chef’s knife and a cutting board, wash and peel the carrots and dice them into small bits. These pieces should be about ¼ to ½ inch in size. Next, wash the celery, cutting off the base of the stalk and chop it in the same way, including the leaves.
In a large Dutch oven, heat the cooking oil until it is hot over medium high heat. Add the vegetables, sautéing them for about five minutes, stirring and turning them. Add the garlic and sauté it with the veggies for about a minute, or until it is golden brown.
Add the chicken broth. Bring the soup to a low boil and add the chicken. Put the lid on the pot and simmer it for about 15 to 20 minutes.
Take the lid off of the pot and test the chicken. It should shred easily and be fully cooked, but if it isn’t, return the lid to the pot and simmer for another five minutes. When the chicken is cooked, remove it to a plate and shred it, removing any gristle and fat, and adding the chicken pieces to the pot.
On a plate or a cutting board, cut the cream cheese into cubes about a half inch square. Then, add these to the pot, stirring them into the soup. They may not easily incorporate into the broth yet, but just let them get warm, and they will soon melt into the soup. Add the frozen spinach, stirring as it thaws to incorporate it into the soup.
If you will be eating the soup right away, you can add the pasta directly to the soup and cook it in the broth. Bring the soup to a boil, add the pasta, and set a timer for 9 minutes. Then add the shredded cheese and stir to allow the cheese to melt. Then, you can scoop the soup out into bowls and serve it, topped with a garnish of Parmesan cheese.
Alternately, if you will not be eating the soup right away, cook the pasta in a separate pot by bringing water to a boil, adding the pasta, and cooking it for 9 minutes. Drain the pasta, cover the pot and set it aside until you are ready to eat. Keep the soup at a simmer on low heat, stirring it occasionally; alternately, you can put the soup into a slow cooker set on low for 6 to 8 hours. Right before serving, stir the pasta and the shredded cheese into the soup, allowing the cheese to melt. Then, serve the soup topped with Parmesan cheese.