Place the chicken in a heavy stock pot and cover it with water. Add 1 teaspoon of salt and 1 teaspoon of pepper, and boil until the chicken is cooked through.
Let the chicken cool and debone it, making sure to reserve the broth.
Using a hand mixer, mix whipping cream, eggs, and 2 teaspoons of salt in a bowl just until blended.
Add enough flour to make a sticky dough.
Place sticky dough on a heavily floured surface.
Knead the dough into the flour until it is no longer sticky.
Once the dough is no longer sticky, begin rolling it out on the floured surface, adding more flour as needed.
Roll the dough paper-thin and cut into small pieces, about two inches by two inches.
Make sure the dough is generously covered in flour, because this will help thicken the broth.
After cutting the dumplings, put them on a plate.
Bring reserved broth to a rolling boil.
Add dumplings one at a time, and allow each dumpling to swirl around in the broth so that it won’t stick to the next dumpling.
Continue adding the dumplings until the broth thickens to the desired consistency.
Add deboned chicken.
Add salt and pepper to taste, and more chicken broth if desired.