PREHEAT the oven to 350° F. Spray 13 x 9-inch baking dish with nonstick cooking spray.
SPRAY large skillet with nonstick cooking spray. Add turkey and onion; heat over medium-high heat or until turkey is no longer pink. Reduce heat to medium. Stir in tomato sauce, oregano, cinnamon, cayenne and 1/4 teaspoon each salt and black pepper; cook, stirring occasionally, until mixture begins to simmer. Simmer for 2 to 3 minutes. Remove from heat.
MEANWHILE, WHISK together flour and 1/4 cup evaporated milk in medium saucepan until smooth. Add additional 2 1/4 cups evaporated milk and remaining 1/2 teaspoon each salt and black pepper; bring to boil over medium heat, stirring frequently. Reduce heat; simmer for 2 minutes, stirring occasionally. Remove from heat. Place egg in small bowl; whisk 1/2 cup hot milk mixture into egg. Whisk milk and egg mixture into saucepan; cook for 1 minute longer until thickened.
COMBINE potato flakes, hot water and remaining 1/2 cup evaporated milk in medium bowl.
LAYER half the eggplant slices on bottom of prepared baking dish. Spoon meat mixture evenly over eggplant; top with 1 cup potato mixture and pour half of white sauce, spreading evenly. Layer remaining eggplant slices over white sauce, top with remaining potato mixture and white sauce. Cover with foil.
BAKE for 45 minutes. Remove foil; sprinkle with cheese. Bake for an additional 10 minutes or until golden and bubbly. Cool for 10 minutes before serving.
• For a more traditional flavor, substitute 1 pound ground lamb for the turkey; drain after cooking.