In a large pot over medium heat, add the chicken, celery with its tops, carrot, onion with its peel, and pepper.
Pour broth over everything and bring it to a boil, then cover, reduce the heat, and let it simmer until the chicken is tender and falls off the bone, about 45 minutes.
While the chicken cooks, make the noodles by mixing eggs, water, oil, salt, and enough flour in a large bowl to form a stiff dough.
Strain the chicken stock, setting aside the meat, celery, and carrots.
Pull the chicken from the bones and return the strained stock, meat, celery, and carrots to the pot, bringing it back to a boil.
Using a broth-dipped spoon, scissors, or your fingers, cut small, chickpea-sized pieces of dough and drop them into the boiling liquid.
The noodles are ready when they rise to the surface.
The noodles are cooked and ready to be served.