Discard the skin and bones from the rotisserie chicken and shred 3–4 cups of meat. Prepare the onion, carrots, celery, and garlic.
Heat the olive oil in an approximately 6-quart Dutch oven over medium-high heat. Add the onion, carrots, celery, and garlic. Cook, stirring often, until the vegetables are just soft, about 8 minutes.
Stir in the chicken, broth, Italian seasoning, kosher salt, and black pepper. Bring to a boil, reduce the heat to medium, and gently boil for 6 minutes.
Add the dried wide egg noodles. Reduce the heat to medium-low and cook for about 6 minutes, until the noodles are tender through the center but still intact. Garnish with parsley and serve hot.