Saute the chopped onions in 3/4 of the oil and 4 1/5 cups (1 liter) water. Add the minced meat and saute until the water evaporates. Add the chopped tomatoes, paprika, black pepper, savory and salt to taste. Cut the thawed phyllo pastry sheets into 6-8 pieces.
Place some of the filling on each piece of phyllo pastry and roll them up, then arrange in a pre-greased oven dish. Smear the top with egg. Bake in a preheated oven at 356°F (180 °C) until browned.
Upon removal, sprinkle it with water and cover them with a lid or cloth to smother.