1. Season the cut up chicken with the kosher salt and black pepper. Lay the pieces in the bottom of a crock pot, skin side up. Pour in the white wine, and then add the chopped onions, carrots and celery. Sprinkle with the dried basil and add the bay leaf.
2. Cover the pot and cook on low for 7 to 8 hours.

To make the noodles:

1. Put the flour in a large mixing bowl. Make a well in the center of the flour and pour in the beaten eggs, salt and the water. With a fork, begin stirring the egg mixture into the flour, gathering it up into a ball when everything is well mixed.
2. Knead the dough with your hands, making sure to gather up all the flour, then cover the dough with a cloth and let it set for about 15 minutes.
3. Flour a work surface and roll the dough out to a thickness of 1/8 inch. With a pizza wheel or the tip of a sharp knife, cut the dough into strips about 3 inches long by 1/2 inch wide.
4. Gather up the noodles and toss them with a bit of flour to keep them separated while they dry. Let them dry a few hours while the chicken is cooking.
5. When the chicken is done, remove the pieces and discard the skin and bones. Pull the meat apart with your fingers and set it aside.
6. Lift out the carrots, onions and celery and set them aside with the shredded chicken. Discard the bay leaf. Keep the chicken and vegetables covered with foil.
7. Pour the cooking liquid from the crock pot into a large soup pot and add the 2 quarts of chicken broth.
8. Bring the liquid to a boil add the noodles. Boil the noodles for about 10 minutes, until they are tender, and then return the shredded chicken and vegetables to the pot.
9. Simmer just until the chicken and vegetables are heated through, and serve hot.