What you'll need:
1 large onion
3 or 4 whole carrots, cut into large pieces
2 or 3 celery stalks, cut into large pieces
3 garlic cloves, peeled
2 bay leaves
1 tablespoon peppercorns
2 tablespoon salt (1 for the broth, 1 for the noodles)
2 cups all purpose flour
2 large eggs
Place the chicken in a large pot. I would recommend at least an 8 quart pot. Place the chopped veggies, garlic cloves, bay leaves, peppercorns, and 1 tablespoon of salt on and around the chicken. Fill the pot with water until it is about 1 inch over the top of the chicken and veggies. Bring to a simmer, cover, and let it go for 2 hours.
Place the flour, eggs, and salt in a large bowl. Stir and slowly add water until you get a stiff dough. Turn dough out onto a large flour sack towel covered lightly with flour. Divide dough into two sections and roll out to about 1/4 inch thick. Use plenty of flour to keep the dough from sticking. Using a pizza cutter cut thin vertical strips and then come back and make horizontal cuts however long you like your noodles. The noodles will puff up while cooking so keep that in mind when cutting. Let rest and dry until the chicken is done.
After 2 hours. Pull the chicken out of the broth. The chicken will literally fall apart. I use tongs and a slotted spoon to get it out. When cool enough to handle separate the meat, skin, and bones. Discard the bones and skin. Set chicken meat aside.
So now we need to strain the broth. Place a large bowl in the sink. Place cheesecloth (or coffee filters torn open :-) ) in a colander. Pour the broth into the colander and let drain into the bowl. Using the back of a spoon push all the juice out of the veggies. Pour the broth into a gravy separator in batches. Then pour only the broth back into the original pot. Discard the fat. Reserve 1 cup of broth for the flour slurry we'll be mixing in at the end. Bring the broth to a boil. In small batches drop in the noodles stirring to make sure they don't stick together. Once they are all in let them boil 20 to 25 minutes.
Add chicken back in and bring back to a simmer. In a small bowl add 1/2 cup of flour to the 1 cup of reserved chicken broth. Whisk. Make sure there are no lumps or your chicken and noodles will be lumpy! Slowly pour the mixture into the broth mixture stirring constantly. Let simmer for a few minutes to thicken.
Voila your done! A little time consuming but so worth it!