Place the chicken wings and vegetables in a large stockpot over medium heat. Pour in only enough cold water to cover (about 3 quarts); too much will make the broth taste weak. Toss in the parsley, bay leaves, and peppercorns, and allow it to slowly come to a boil.
Lower the heat to medium-low and gently simmer for about 1-½ hours, partially covered. 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.
When the stock is finished cooking, you can either discard the chicken wings with the vegetables or remove them to a bowl, wait until they are cool enough to handle, and remove the meat to add to the soup. Discard the skin and bones.
Carefully strain the stock through a fine colander into another pot to remove the vegetables. At the point, you can use the stock immediately for the soup or if you plan on storing it, place the pot in a sink full of ice water and stir to cool down the stock. Cover and refrigerate for up to one week or freeze.
For the soup:
Place a soup pot over medium heat and add the oil and coat the pan.
Add the onion, garlic, carrots, celery, and bay leaf. Cook and stir for about 5 minutes, until the vegetables are softened but not browned.
Add the stock, chicken thighs, and parsley. Stir to combine and bring to a boil.
Lower the heat and simmer for 15-20 minutes until or until the chicken is cooked through and the vegetables are tender.
Meanwhile, cook the pasta or noodles of your choice and drain.
Carefully remove the chicken to a cutting board and using a fork and knife, cut the chicken into bite-sized pieces and carefully, return to the soup.
Discard the bay leaf from the soup.
Add the pasta to bowls and cover with soup to serve.