In a large stockpot or Dutch oven over medium heat, add the olive oil. Next, add the carrots, celery, garlic, bay leaf and onions. Saute until the vegetable begin to wilt, about 5 minutes. Next, add the cherry peppers and lemon peel and continue to saute for another 2 minutes. Add in the chicken stock and chicken pieces and sprinkle with smoked salt, if using, and pepper. Bring the soup to a gentle simmer and cook, about 30 minutes.
Remove the chicken to a plate and wait until the pieces are cool enough to handle. Either with 2 forks or with your hands, pull the meat from the bone and shred, taking care to remove any cartilage. Once all of the meat is pulled from the bone, add the meat back to the soup and discard the bones.
In the meantime, add the potatoes to the soup, cover and continue to cook and additional 15 minutes. Taste the soup again for seasoning, adding more salt and pepper, if necessary. Add in the noodles. Serve the soup in warmed bowls. Garnish with a squeeze of lemon and some parsley.