Put the stale bread into a large mixing bowl. Add the milk, the eggs, as well as salt, pepper, and nutmeg. Mix well and let it rest for at least two hours, covered with a tea towel, in a cool place or in the fridge. Stir occasionally to ensure that the mix absorbs the liquid uniformly. After the two hours, add the flour, then the parsley, and the cheese. Mix gently. Finely chop the onion and fry it in oil and butter for ten minutes at medium heat, stirring occasionally. Let the onion cool off, then incorporate it into the mix. Let the mixture rest for another half an hour covered with a tea towel. It should look uniformly moist and slightly sticky. Using your hands, form the canederli by pressing together enough of the mix to make balls the size of a small orange. You should be able to produce 14-16 balls out of the entire mix. After making each ball, roll it in flour to seal the outside and prevent the canederli from sticking to each other. When all the canederli are ready, re-roll them into flour and compress them a second time. Have the vegetable stock in a large pot, well boiling on the stove. Place the canederli gently in the pot (12-13), wait until the boil is resumed. Boil the canederli for 12-15 minutes (they will be floating the whole time), then drain them gently. If serving the canederli "dry", warm up the butter just enough to melt it. Place 3 canederli into each plate, pour the melted butter on them, then sprinkle with some thin-sliced chives, a generous amount of grated Parmigiano, and some freshly ground black pepper. If serving the canederli in broth, prepare more vegetable stock (as the one used for boiling will be cloudy because of the flour). Place one or two canederli into each bowl, then pour the broth on them. Finish with some grated Parmigiano and (optional) chives.