Chop the onion, carrots, and celery; mince the garlic.
Warm the olive oil in a large pot over medium heat.
Sauté onion, carrots, and celery until lightly softened, about 5–6 minutes.
Stir in garlic, tomato paste, Italian seasoning, and red pepper; cook 1 minute until fragrant.
Pour in chicken broth and diced tomatoes; add Parmesan rind if using. Bring to a gentle boil.
Lower heat and simmer 10–12 minutes to build flavor. Season with salt and pepper.
Stir in the shredded chicken and return to a simmer.
Add egg noodles and cook until tender, 6–8 minutes. Remove Parmesan rind.
Finish with lemon juice and parsley. Taste and adjust seasoning before serving.
Ladle into bowls and top with grated Parmesan.