In large skillet, heat oil and butter; saute onion until golden. Add parsley, garlic, beef, cinnamon, salt and pepper. Cook until meat is lightly browned. Stir together wine and tomato paste; blend into meat mixture. Add water and simmer 20 minutes or until most of the liquid has been absorbed. Cool. Blend beaten egg whites into cooled meat, set aside.
Slice eggplant and brush each side with oil. Sprinkle each side with salt and pepper. Broil, turning once, until golden brown on both sides.
BECHAMEL- In medium sauce pan melt butter over low heat; blend flour until smooth. Gradually blend in milk. Add salt. Cook, stirring constantly until thickened and smooth. Remove from heat. Gradually beat egg yolks into sauce. Add cheese and set aside.
Sprinkle bread crumbs evenly over bottom of pan(8x8x2). Arrange a layer of eggplant slices; cover entire surface with half meat mixture. Arrange another layer of eggplant and remaining meat mixture. Top with remaining eggplant. Pour bechamel sauce over all. Bake at 350 for 1 hour or until top is golden brown. Cool slightly. Cut into squares and serve.