Heat the oil in a large skillet and fry onion, shallot and celery for 5 minutes. When the onion is translucent, add the meat and break it up with a wooden spoon to avoid lumps. When the meat is pinkish, pour in the white wine and add the parsley, salt and pepper. Allow the juice to evaporate and cook for about 10 minutes. Remove from the heat and let cool. Mix in the beaten egg and set aside in a cool place.
In a large bowl, combine flour, salt, eggs and water. Knead for about 10 minutes. Add a little water if the dough is too stiff, or a little flour if it is too sticky.
On a lightly floured surface, roll out the dough, and cut circles about 6 cm in diametre. Place 1 tablespoon of meat filling on one side of each circle, and fold the dough over the filling to cover it completely and obtain half-moons. Seal the edges with a little water.
Boil salted water in a saucepan and gently drop the kreplach into the water, about 5 at a time. Cook until the kreplach float to the surface, a total of 3 to 4 minutes. Take them out with a slotted spoon.
To serve, reheat the kreplach for a few minutes in simmering chicken broth. Serve with the stock.