Spread sliced rolls onto 2 baking sheets, and bake until slightly dry (12 minutes). Transfer to a large bowl and set aside.
Heat oil in a 4 qt saucepan over medium-high heat. Add onion, and cook, stirring occasionally, until golden brown (10 minutes). Transfer to the bowl with the bread and set aside.
Add milk to the saucepan; bring to a boil over high heat, and pour over bread. Add parsley, flour, nutmeg, and eggs. Season with salt and pepper, and using your hands, mix until evenly combined.
Bring an 8 qt saucepan of salted water to a boil over high heat. Moisten hands with cold water, and form bread mixture into 2 inch balls and set aside.
Working in batches, add balls to boiling water, and cook until firm (15 minutes). Using a slotted spoon, drain briefly on paper towels, and transfer to a serving platter. Sprinkle with parsley and serve in bowls surrounded by gravy.