Simmer: Place all the ingredients in a very large pot, cover with the water, and bring to a boil. Turn the heat to very low, skim the foam if necessary and leave to simmer very gently, uncovered, for about 6 hours.
Strain the stock, keep the meat, and discard the rest. You could keep the carrots as well if you make the semolina dumpling soup immediately. Otherwise, discard.
Boil: Place the stock in a clean pot and bring it again to a boil. Let boil rapidly for about 10 minutes. Adjust the taste with salt and pepper.
Store: If you want to keep the broth for several days, fill it in clean bottles or jars. Place the lid on immediately and leave to cool completely. It will keep in the fridge for several days. To keep it longer, place it into smaller containers, and freeze.
Boil: Pour about 1 ½ liter of the stock in a soup pot. Peel the carrots and chop them into slices. Add them to the stock and bring everything to a boil.
Beat eggs: In the meantime, make the dumplings. Separate the egg. Beat the egg white with the salt until it is pretty stiff but not as stiff as you would need them for baking. Add the egg yolk and the vegetable oil and incorporate them carefully.
Add the semolina two tablespoons at a time and fold it in gently. After adding 6 tablespoons of the semolina, the consistency should not be pourable anymore, and you should be able to trace marks on it with the fork. Add a maximum of one level tablespoon semolina if you think that the batter is too soft. Leave to stand for 5 minutes.
Form dumplings: The soup should be boiling now. Turn the heat down to medium-low and add ½ cup cold water to the stock. Add the dumplings to the soup using a teaspoon, fill about ½ -3/4 of the teaspoon with batter and let it glide into the soup (you should immerse the teaspoon in the soup before starting).
Cook dumplings: Cover the pot, leaving a crack open and cook the dumplings until soft; it should take about 10 – 15 minutes, but don't worry too much if it takes a bit longer. You can also turn off the heat when they are almost done, put on the lid, and leave the pot on the stove for a while. They will continue cooking in the soup and become soft and fluffy.
Adjust the taste again and sprinkle some fresh parsley on top.
OR chicken carcasses and 500 g/ 1.1 lb giblets OR chicken carcasses and 2 whole chicken legs.