Bring two cups of chicken broth to a boil and add chicken breast. Turn heat to medium and cook for twenty minutes. Use a meat thermometer, and it's done at 165 degrees. Place on a plate and let cool.
Slice ham as thin as possible and no more than three inches long.
Soak the dried mushrooms in hot water, and let sit for twenty minutes. Check to see that they have softened, and if not, drain the water and add more hot water.
When softened, rinse under cool water, squeezing out excessive water. Slice into thin slices.
Rinse the white mushrooms and slice thinly.
Using two forks, shred the chicken.
Cut the green onion into thin slivers. Add one tsp of oil into a skillet and add the scallions and white mushrooms. Saute until the mushrooms slightly start to brown. Place the 1 1/2 quarts of chicken broth in the stock pot. Add the chicken, ham, both types of mushrooms, and green onions.
Heat on medium and add the sesame oil and white pepper.
Fill the Dutch oven halfway and cook according to the directions on the pasta. Use only enough pasta for your number of servings.
Add the pasta to a large bowl for each serving, and add enough soup to cover the pasta. Serve.