For the stock: In a large stock pot, add carrots, celery, onions, parsley and peppercorns. Break up the chicken carcass into several smaller pieces and add to pot. Add enough water to completely cover ingredients and bring to a simmer. Cook for 1 1/2 hours.
Remove veggies and chicken pieces, and strain stock through a sieve or paper towel. Salt to taste. Allow to cool completely, then store in fridge for up to 3 days or in freezer for up to 1 month.
For the soup: In a large stock pot over medium heat, add oil. When hot, add carrots, onion and celery. Add salt to taste. Sauté for 5 to 7 minutes.
Add chicken breast and stir to combine. Add the stock and pasta. Bring to a boil and cook for 7 to 8 minutes until pasta is cooked through.