In a large saucepan, melt the butter. Add the onion and cook over moderate heat until softened, about 3 minutes. Stir in 8 cups of the chicken stock and bring to a simmer. Season with salt and white pepper to taste.
Meanwhile, in a medium saucepan, combine the remaining 1 cup stock with the thyme, nutmeg, half teaspoon salt and a pinch of white pepper. Bring to a boil over high heat. Remove from the heat and beat in the flour until thoroughly blended. Let the mixture cool slightly, then beat in the eggs, one at a time.
Drop tablespoons of the dumpling mixture into the simmering soup and cook until the dumplings begin to firm, about 5 minutes. Remove from the heat, cover the saucepan and set aside to steam the dumplings for 3 minutes before serving.