In a medium pot, combine 1 1/2 quarts of chicken stock, chicken breast, 1/2 onion, 1 peeled carrot, 1 celery stalk, 1 peeled parsnip, and a handful of parsley sprigs. Bring to a boil and then turn down to a gentle simmer and cook for 40 minutes.
Turn the broth off, remove the chicken to a plate, and discard all the vegetables. Season the broth with salt and pepper to taste. When the chicken has cooled, shred the meat into bite-size pieces and discard the bone and skin. Set aside.
In another medium pot, add diced carrot, celery, and onion. Cover with the hot broth and cook at a simmer until the vegetables are cooked through and tender. While these vegetables are simmering, cook your pasta in a separate pot filled with water, as instructed on the package, strain, and set aside. Once the vegetables are finished cooking, add the shredded chicken, dill, and pasta. Taste and season with salt and pepper if necessary.