In a large bowl, beat the egg, milk, cornstarch, onion, salt, pepper, nutmeg, allspice and ginger. Add beef; mix lightly but thoroughly. Shape into 1-1/2-in. meatballs. (Mixture will be very soft. For easier shaping, rinse hands in cold water frequently.)
In a large skillet over medium heat, brown the meatballs in butter, half at a time, for about 10 minutes or until no longer pink. Remove meatballs to paper towels to drain, reserving 1 tablespoon drippings in skillet.
For gravy, add butter to drippings. Stir in flour. Add broth and milk. Bring to a boil; cook and stir for 2 minutes or until thickened. Season with salt and pepper. Return meatballs to skillet; heat through on low. Garnish with parsley if desired.