Place the chicken, including neck and back, in a large soup pot. Add 3 quarts water, the onions, carrots, celery, parsnips, garlic, 1 teaspoon salt and 1/2 teaspoon pepper. Bring to a boil, cover partially, lower the heat and simmer for 1 hour.
Transfer the chicken breasts and legs to a plate and the carrots, celery and parsnips to a bowl. Remove the chicken meat from the bones and return the bones and skin to the pot. Add the parsley stems; simmer for 45 minutes. Strain the broth into a saucepan; discard the solids. Skim the fat from the surface. Keep warm over low heat.
Meanwhile, shred the chicken; cut the vegetables into small cubes.
In a large pot of boiling, salted water, cook the noodles until al dente; drain. Add the noodles, chicken and vegetables to the broth; stir in the chopped parsley.