Sauté the celery, carrots, and onion with the olive oil and butter in a large soup pot over medium-high heat for 5 to 7 minutes.
Stir in the garlic and cook for about 30 seconds.
Stir in the flour and cook for about 1 minute.
Pour in the chicken broth and stir until the flour dissolves. Add the chicken, Italian seasoning, and cream. Bring the soup to a slight boil, then cover with the lid slightly open.
Reduce the heat so the soup simmers gently and cook for 10 minutes.
Stir in the egg noodles, cover the pot again with the lid slightly open, and cook for 8 to 10 minutes, stirring halfway so the noodles do not stick.
Remove the chicken, cut it into bite-size pieces, and return it to the pot. Season with salt and pepper, stir in the parsley, and serve immediately.