Heat one tablespoon of the butter in a large skillet over moderate heat and cook the meat, carrots, and onions until the meat is browned and the carrots are tender. Drain the meat in a colander, then place in a mixing bowl. Add the salt, pepper, nutmeg, lemon juice, and parsley and stir to combine. Set the meat mixture aside.
Heat the remaining 3 tablespoons (45 ml) of butter in a saucepan over moderate heat and stir in the flour to make a roux. Cook this for 2 to 3 minutes, then add the beef broth or milk. Continue heating, stirring constantly, until the sauce boils and becomes quite thick. Combine the sauce with the meat mixture, stirring to combine them thoroughly, and chill this mixture for at least two hours in the refrigerator, until it has become solid. When the mixture has solidified, roll it into balls about 1 inches (2.5 cm) in diameter, using your hands.
Roll the balls in the bread crumbs, then in the egg and water mixture, then in the bread crumbs again. Fry a few at a time in a deep fryer with at least 2 inches (5 cm) of oil at 375F (190C) until golden (about 2 to 3 minutes). Drain on paper towels and serve immediately.
Reproduced by permission of Worldwide Recipes.