Place the chicken and vegetables in a large stockpot over medium heat. Pour in only enough cold water to cover; too much will make the broth taste weak. Toss in the thyme, bay leaves, and peppercorns, and allow it to slowly come to a boil. Lower the heat to medium-low and gently simmer until chicken is done. If chicken cooks quickly, remove and let remaining vegetables simmer until an hour has passed. As it cooks, skim any impurities that rise to the surface; add a little more water if necessary to keep the chicken covered while simmering.
Carefully remove the chicken to a cutting board. When its cool enough to handle, hand-shred the meat.
Carefully strain the stock through a fine sieve into another pot to remove the vegetable solids. Discard the vegetables and set aside the stock for the soup.
Soup:
Place a soup pot over medium heat and coat with the oil. Add the onion, garlic, carrots, celery, thyme and bay leaf. Cook and stir for about 6 minutes, until the vegetables are softened but not browned. Put in 2 cups of water and boil until vegetables are softened, adding more water if necessary. Pour in the chicken stock and bring the liquid to a boil. Add the noodles and cook until tender. Fold in the chicken, and continue to simmer for another couple of minutes to heat through; season with salt and pepper. Sprinkle with chopped parsley before serving.