Heat 1 tablespoon of oil in a skillet, add the onion, and stir-fry over moderate heat for 2 minutes. Add the beef, salt, and pepper, and stir-fry for 5 minutes. Add the egg and parsley and fry for 1 minute more. Cool well.
Take 1 phyllo sheet and spread it out flat with a short end nearest you. Place 2 heaping tablespoons of the beef mixture 2 inches in from the short edge. Fold both long sides in toward the middle, beginning with the short end roll the phyllo to shape a packet 4 inches long and 1 1/2 inches wide.
Repeat with the remaining phyllo sheets and stuffing. Set aside. Put the balance of the oil in a skillet over moderately low heat and add the rolls. Brown on both sides for about 3 minutes; the low heat prevents the very thin pastry sheets from burning. Drain the rolls on paper towels for a minute.