Separate the thighs from the drumsticks and skin each piece. Put in a large soup pot and cover with the water and broth. Bring to a simmer. Add spices, onion and celery. Simmer until chicken is tender (about 40 mins).
Remove chicken from stock and set aside. Bring to a boil and add spaghetti; it should come out very moist (the spaghetti will absorb some of the broth); cook until tender, about 8 mins.
Take the meat off the bones and add to the spaghetti. Fold in pimentos and black olives. Sprinkle on the parmesan cheese and toss until all is incorporated. Serve with crusty bread.