In a 5 qt Dutch oven, combine chicken and water. Bring to a boil. Reduce heat; cover and simmer 15 minutes.
Now is a good time to mix the noodles.
Basic Noodles: Lightly spoon flour into a measuring cup and level off. In a small bowl, combine flour and salt; blend well. Make a well in the center. Add water, oil, and egg. Gradually work the flour into the liquid to form a dough. On a floured surface, knead the dough 2-3 minutes. Wrap the dough in a plastic bag and let rest at room temperature for 1 hour.
Once the chicken has simmered 15 minutes, skim off any scum that has risen to the surface. Add bouillon cubes, 1/2 cup onion, salt, pepper, and bay leaf. Simmer an additional 35 to 45 minutes or until the chicken is tender.
Remove chicken from the broth to remove the meat from the bones; cut the chicken into bite-size pieces. Skim the fat from the broth. Return chicken to the pot. Stir in celery, carrots, and 1/4 cup onion. Simmer 15 minutes or until the carrots are tender crisp.
If you are making your own noodles:.
While the vegetables are cooking; on a floured surface, roll out the noodle dough as thin as possible keeping the dough in a rectangular shape. Slice the dough into 1/4 inch slices into the length that you want. Hint: fold the rolled dough into thirds and slice through the thickness to save time.
Once the carrots are tender crisp, remove the bay leaf. Bring the soup back to a boil. Drop noodles into boiling soup. Cook uncovered 5 - 10 minutes or until noodles are tender, stirring occasionally.