Wash the chicken, remove and wash the giblets and neck, if included, and place everything in a large pot. Fill about ¾ full of water, add salt, place over medium high heat, and bring to a boil.
When scum starts to appear, remove it with a spoon, and discard. Lower the temperature, so that the soup is simmering gently.
Let the soup simmer for an hour to an hour and a half, then remove from heat.
Using a flat metal strainer, lift the chicken out of the pot and place on a plate. Remove the giblets and neck, if they are also in the soup.
Strain the broth into another pot, taste for salt, adding more to taste (I can guarantee that it will need more salt at this point) then place half of the broth into a container to freeze for another time. (Use the chicken to make chicken pot pie (recipe coming soon), chicken salad, or any way you like. You may also add some pieces of chicken to the soup.)
About 10 minutes before you want to serve the soup, cook the pastina in a separate pot until al dente (you can cook the pasta directly in the broth, but it will make the soup cloudy. If you don’t mind it not being clear, and you don’t want to wash another pot, just cook the pastina right in the broth.)
When the pastina is ready, drain the water and add it to the simmering broth. Add the stracciatella, if using. (Stracciatella recipe below.)
Taste for salt again, and add some black pepper if desired, and serve.