Wash the parsley (put four leaves aside) and chop finely. Bring milk, salt and fat to the boil. Add the flour at once and stir until the dough comes off the bottom of the pot as a lump.
Take it off the stove. Stir in the egg with the dough hooks of the hand mixer. Cut off small dumplings. Let them simmer in the boiling broth for about 10 minutes. Garnish with parsley.