Step 1Heat the oven to 300 degrees. Spread the cubes on 1 or 2 rimmed baking sheets, and toast until very dry, about 12 minutes. Transfer the bread to a large bowl. Stir in the eggs and parsley until the bread cubes are coated, and set aside.
Step 2In a large saucepan, melt the 5 tablespoons butter over medium heat. Add the onion and cook, stirring occasionally, until the onion is softened and lightly colored, 10 to 12 minutes. Stir in the milk, scraping any flavoring from the bottom of the pan, and bring the milk to a boil over high heat. Remove from heat and pour the milk over the bread. Season with 1 teaspoon salt, or to taste, and the nutmeg, and toss well to combine.
Step 3Cover and refrigerate the bread until it has soaked up the milk and is softened, about 45 minutes.
Step 4Bring a large pot of salted water to boil over high heat. Moisten your hands with cold water, and form the bread mixture into 2- to 2½-inch balls (if the mixture feels a bit dry, add warm milk, a little at a time, and work it into the mixture). Gently add the dumplings (this will need to be done in batches), cover and boil them for 15 minutes, then reduce the heat and leave to poach in the water an additional 10 minutes. Transfer to a serving platter and garnish with chopped parsley, melted butter and chives.