Cut the bread into very fine slices. Heat 1 tablespoon each of the oil and butter in a pan, and toast about 1/3 of the slices of bread for 3-4 minutes at moderate heat, turning once or twice. Salt and pepper the bread, and put it in a bowl.
Peel the onion and garlic, and chop them finely. Wipe the crumbs out of the pan with a paper towel. Heat the remaining butter and the second tablespoon of oil, add the garlic and onion, and seat them for 2-3 minutes. Then add the parsley, and continue cooking for another 2-3 minutes.
Put the rest of the bread into a bowl and sprinkle the milk over it. Add the onion-parsley mixture. Season with salt, pepper, and mace, and blend gently (do not knead!). Allow to stand for at least 10 minutes.
Beat the eggs in a bowl. Add the eggs and toasted bread ti the dough, and stir carefully. If the dough i still too soft, you can add some pastry flour to make it firmer. Fill a large pot with water, and bring it to a boil. Salt the water. Wetting your hands, take a handful of the dough and shape it into smooth, round dumplings. Wrap each one first in plastic wrap and then in aluminum foil. Place the wrapped dumplings in the boiling water, and simmer for 15-20 minutes at low heat.