Heat olive oil in a large saucepan over medium heat. Add onion and 1/2 tsp of salt and cook, stirring occasionally, until onion is very soft, about 10 minutes. Stir in turmeric and cook a minute, then add chicken, broth, water, parsley, and another 1/2 tsp of salt. Bring to a boil then cover and simmer until chicken is cooked through, about 15 minutes. Remove chicken from the soup using a slotted spoon and transfer to a cutting board.
Add the noodles to the soup (if using spaghetti, break it into thirds or quarters). When chicken is cool enough to handle, shred it with two forks or chop coarsely with a knife. Return chicken to pot and continue cooking until noodles are tender. Taste and add another 1/2 tsp salt as needed.