In a large bowl, combine the bread with enough warm milk to saturate. (You may not need all of the milk.) Let soak for 30 minutes.
In a medium skillet, heat the butter over medium heat. Add the onions and sauté until soft and translucent, about 5-10 minutes. Season with a few pinches of salt, a few turns of freshly ground black pepper, nutmeg, and parsley. Transfer the onion mixture to the bread mixture.
Add half the beaten eggs to the bread mixture and mix with your hands. Continue adding egg and lightly kneading until a wet dough forms. If the dough is too sticky, add a little flour or breadcrumbs. Set aside to rest at room temperature for 10 minutes.
Bring a large pot of salted water to a boil over high heat. Use damp hands to form 2-inch balls with the bread mixture. Working in batches, lower the knödel into the boiling water and cook until firm, about 15 minutes. Using a slotted spoon, transfer to a plate lined with a clean towel to drain.